Version pdf de ce document

Premia 14

The underlined algorithms have been already implemented.

1 Standard European Options in the Black-Scholes Model

1.1 Call, Put, CallSpread, Digit

1.1.1 Analytic

1.1.2 Tree

1.1.3 Finite-Difference

1.1.4 Montecarlo

2 Standard American Options in the Black-Scholes Model

2.1 Call, Put, CallSpread, Digit

2.1.1 Tree

2.1.2 Finite-Difference

2.1.3 Montecarlo

2.1.4 Approximation

3 Barrier European Options in the Black-Scholes Model

3.1 Call, Put In-Out/Down-Up, Parisian

3.1.1 Analytic

3.1.2 Trees

3.1.3 Finite-Difference

3.1.4 Montecarlo

3.2 Discrete Barrier Option

3.2.1 Approximation

3.2.2 Montecarlo

4 Barrier American Options

4.1 Call, Put In-Out/Down-Up

4.1.1 Trees

4.1.2 Finite-Difference

5 Double Barrier European Options In/Out, Parisian in the Black-Scholes Model

5.1 Call, Put In/Out

5.1.1 Analytic

5.1.2 Approximation

5.1.3 Trees

5.1.4 Finite-Difference

5.1.5 Montecarlo

6 Double Barrier American Options In/Out in the Black-Scholes Model

6.1 Call, Put In/Out

6.1.1 Trees

6.1.2 Finite-Difference

7 Lookback European Options in the Black-Scholes Model

7.1 Call, Put Fixed-Floating

7.1.1 Analytic

7.1.2 Trees

7.1.3 Finite-Difference

7.1.4 Montecarlo

8 Lookback American Options

8.1 Call, Put Fixed-Floating

8.1.1 Trees

8.1.2 Finite-Difference

9 European Asian Options in the Black-Scholes Model

9.1 Call, Put Fixed-Floating

9.1.1 Approximation

9.1.2 Trees

9.1.3 Finite-Difference

9.1.4 Montecarlo

9.1.5 Approximation

10 American Asian Options in the Black-Scholes Model

10.1 Call, Put Fixed-Floating

10.1.1 Trees

10.1.2 Finite-Difference

11 Europeen nD Standard Options in the Black-Scholes Model

11.1 CallMax, PutMin, BestOf, Exchange

11.1.1 Analytic

11.1.2 Tree

11.1.3 Finite-Difference

11.1.4 Montecarlo

12 American nD Standard Options in the Black-Scholes Model

12.1 CallMax, PutMin, BestOf, Exchange

12.1.1 Tree

12.1.2 Finite-Difference

12.1.3 Montecarlo

12.1.4 Sparse Grid

13 Standard European Options in the Merton Model

13.1 Call, Put, CallSpread, Digit

13.1.1 Analytic

13.1.2 Approximation

13.1.3 Finite-Difference

13.1.4 Montecarlo

14 Standard American Options in the Merton Model

14.1 Call, Put, CallSpread, Digit

14.1.1 Finite-Difference

15 Standard European Options in the Dupire-Local Volatility Model

15.1 Call, Put, CallSpread, Digit

15.1.1 Finite-Difference

15.1.2 Montecarlo

15.1.3 Approximation

16 Standard European Options in the Hull-White,Stein,Scott Model

16.1 Call, Put, CallSpread, Digit

16.1.1 Montecarlo

17 Standard European Options in the Heston Model

17.1 Call, Put, CallSpread, Digit

17.1.1 Montecarlo

17.1.2 Finite Difference

17.1.3 Tree

18 Standard European Options in the Bergomi Model

19 Standard European Options in the Foque Papanicolau Sircar Model

20 Standard European Options in the Multi-Factor Foque Papanicolau Sircar Model

21 Standard European Options and Barrier Options in Exponential LÚvy models

Fourier transform [224],[143] and Finite difference methods [193],[238],Wiener-Hopf[174], Closed Formulas for pricing American, Barrier options and Lookback options in Kou model [128],[129], Pricing Fast pricing of American and barrier options under Levy processes[218], Tree methods[141]

22 Path Dependent Options in Exponential LÚvy models

23 Standard European Options in Stochastic volatility models with jumps

24 Pricing European options in affine jump-diffusion

25 Calibration in the Dupire Model

26 Calibration in Stochastic Volatility and Jump Model

27 Pricing Interest Rate Derivatives

27.1 Zero-Coupon Bond,Coupon Bearing,European, American Option on ZCB,Cap/Floor,Swaptions, Bermudan Swaptions

27.1.1 Vasicek,Hull-White,Hul-White 2D

27.1.8 Hunt Kennedy Pellser Markov-functional interest rate models

27.1.9 Affine Models

27.1.10 Multi-factor quadratic term structure models

28 Calibration Interest Rate Derivatives

29 Pricing Inflation Derivatives

30 Pricing Credit Risk Derivatives

30.0.11 Credit Default Swaps:Models Reduced form approaches on single name

30.0.12 CDO

31 Pricing Energy Derivatives

31.0.13 Swing Options

32 Pricing Volatility Product

32.0.14 Variance/Volatility Swap,Options on Realized Variance/Volatility

33 Pricing Insurance Derivatives

34 Risk


[1]    Y.S.Kim, S.Rachev, M.S.Bianchi, F.J.Fabozzi. Computing var and avar in infinitely divisible distributions. Probability and Mathematical Statistics, 30(2), 2010.

[2]   A. Herbertsson. Default contagion in large homogeneous portfolios. No 272, Working Papers in Economics from G├Č┬űteborg University, Department of Economics, 2008.

[3]   A Tree-based Method to price American Options in the Heston Model. Vellekoop, m.h. and nieuwenhuis, j.w. Journal of Computational Finance, to appear, 2009.

[4]   A.Ahdida A.Alfonsi. A mean-reverting sde on correlation matrices. Preprint.

[5]   A.Alfonsi. A second-order discretization scheme for the cir process: application to the heston model. Preprint CERMICS hal-00143723.

[6]   H. NIEDERREITER A.B.OWEN and J.SHIUE Editors. Randomly permuted (t,m,s)-Nets and (t,s)-sequences. in "Montecarlo and Quasi Montecarlo methods in Scientific Computing". Springer, New York, 1995.

[7]   M.Mnif A.B.Zeghal. Optimal multiple stopping and valuation of swing options in levy models. Int. J. Theor. and Appl. Finance, 9(8):1267–1297, 2006.

[8]   A.Kawai. Analytical and monte carlo swaptions pricing under the forward swap measure. Journal of Computational Finance, 6-1:101–111, 2002.

[9]   A.Kohatsu Higa P.Tankov. Jump-adapted discretization schemes for levy-driven sdes. To appear in Stochastic Processes and their Applications, 2011.

[10]   A.Kolodko J.Schoenmakers. Iterative construction of optimal bermudan stopping time. Finance & Stochastics, 10:27–49, 2006.

[11]   A.Li P.Ritchken L.Sankarasubramanian. Lattice methods for pricing american interest rate claims. The Journal of Finance, 50:719–737, 1995.

[12]   G.Fusai A.Meucci. Discretely monitored asian options under l├Č┬ľvy processes. J. Banking Finan., 2008.

[13]   S. Antonelli, F. Scarlatti. Pricing options under stochastic volatility : a power series approach. Finance Stoch., 13:269–303, 2009.

[14]   A.PELSSER-T.VORST. The binomial model and the greeks. The Journal Of Derivatives, Spring:45–49, 1994.

[15]   S.Crepey A.Rahal. Pricing convertible bonds with call protection. Journal of Computational Finance, to appear, 2011.

[16]   A.Sepp. Pricing european-style options under jump diffusion processes with stochastic volatility: Applications of fourier transform. Proceedings of the 7th Tartu Conference on Multivariate Statistics, 2004.

[17]   A.Sepp. Pricing options on realized variance in the heston model with jumps in returns and volatility. Journal of Computational Finance, 11-4, 2008.

[18]   G.FUSAI A.TAGLIANI. Accurate valuation of asian options using moments. International Journal Of Theoretical and Applied Finance, 2.

[19]   B.Lapeyre A.Turki. SIAM J. Financial Math. to appear, 1, 2012.

[20]   A.Van Haastrect A.Pelsser. Efficient, almost exact simulation of the heston stochastic volatility model. Preprint, 2008.

[21]   J.HULL A.WHITE. The pricing of options on assets with stochastics volatility. J.Of Finance, 42:281–300, 1987.

[22]   J.HULL A.WHITE. The use of the control variate technique in option pricing. J.Of Finance and Quantitative Analysis, 23:237–251, 1988.

[23]   J.HULL A.WHITE. Efficient procedures for valuing european and american path-dependent options. The Journal of Derivatives, 1:21–31, 1993.

[24]   A.ERN S.VILLENEUVE A.ZANETTE. Adaptive finite element methods for local volatility european option pricing. International Journal of Theoretical and Applied Finance, 7(6), 2004.

[25]   O.Kudrayavtsev A.Zanette. Efficient pricing of swing options in lÚvy-driven models. preprint.

[26]   S.VILLENEUVE A.ZANETTE. Parabolic A.D.I. methods for pricing american option on two stocks. Mathematics of Operations Research, pages 121–151, Feb 2002.

[27]   Etore P. Jourdain B. Adaptive optimal allocation in stratified sampling methods. Preprint Cermics hal-00192540, pages 1–25.

[28]   Ole Barndorff-Nielsen and Neil Shephard. Non-gaussian ornstein–uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society, 63(2):167–241, 2001.

[29]   B.Arouna. Robbind-monro algorithm and variance reduction. Journal of Computational Finance, 7-2:335–362, 2003-04.

[30]   B.Dupire. <pricing on a smile. Risk magazine, 7:18–20, 1994.

[31]   B.Jourdain A.Zanette. Moments and strike matching binomial algorithm for pricing american put options. Decis. Econ. Finance, (31), 2008.

[32]   B.LAPEYRE, A.SULEM, and D.TALAY. Understanding Numerical Analysis for Financial Models. Cambridge University Press, To appear.

[33]   P.JAILLET D.LAMBERTON B.LAPEYRE. Variational inequalities and the pricing of American options. Acta Applicandae Mathematicae, 21:263–289, 1990.

[34]   C. Kahl, P.Jackel. Fast strong approximation monte-carlo schemes for stochastic volatility models. Journal of Quantitative Finance, 6:513–536, 2006.

[35]   P. CARR. Randomization and the american put. Technical report, Morgan Stanley Bank - New York, 1997.

[36]   P. Carr and L. Wu. Static Hedging of Standard Option. Technical report, 2004.

[37]   Peter Carr, HÚlyette Geman, Dilip B. Madan, and Marc Yor. Pricing options on realized variance. Finance Stoch., 9(4):453–475, 2005.

[38]   Peter Carr and Dilip B. Madan. Saddlepoint methods for option pricing. Journal of Computational Finance, 2011 to appear.

[39]   C.C.W.Leentvaar C.W. Oosterlee. The effect of coordinate transformations for sparse grid pricing of basket options. Preprint, to appear JCAM, 2007.

[40]   Kyriakou I. Cerny, A. An improved convolution algorithm for discretely sampled asian options. Quantitative Finance to appear, 2010.

[41]   J.F. Chassagneux and S. Cr├Č┬ľpey. Doubly reflected BSDEs with Call Protection and their Approximation. Preprint, 2010.

[42]   C.Labart J.Lelong. Pricing double barrier parisian options using laplace transforms. preprint CERMICS, 2006.

[43]   R. Carmona S. Crepey. Monte carlo computation of small loss probabilities. Technical report, Preprint, 2008.

[44]   C.Rogers P.Di Graziano. A dynamic approach to the modelling of credit derivatives using markov chains. Preprint, 2006.

[45]   N.Hilber A.M.Matache C.Schwab. Sparse wavelet methods for option pricing under stochastic volatility. Journal of Computational Finance, 8(4):1–42, 2005.

[46]   G.FUSAI D.I.ABRAHAMS C.SGARRA. An exact analytical solution for discrete barrier options. Working Paper SEMEQ Department University Piemonte Orientale Italy, 2004.

[47]   C.W.CRYER. The solution of a quadratic programming problem using systematic overrelaxation. SIAM J. Control, 9:385–392, 1971.

[48]   C.W.CRYER. The efficient solution of linear complementarity problems for tridiagonal minkowski matrices. ACM Trans. Math. Softwave, 9:199–214, 1983.

[49]   D.Belomestny J.Schoenmakers. A jump-diffusion libor model and its robust calibration. Preprint, 2006.

[50]   D.Belomestny Mathew J.Schoenmakers. A stochastic volatility libor model and its robust calibration. Preprint, 2007.

[51]   P. CARR D.B.MADAN. Option valuation using the fast fourier transform. Journal of Computational Finance, 2(2):61–73, 1998.

[52]   D.Brigo A.Alfonsi. Credit default swap calibration and derivatives pricing with the ssrd stochastic intensity model. Finance & Stochastics, 9, 2005.

[53]   D.Brigo P. Pallavicini Torresetti. Calibration of cdo tranches with the dynamical generalized-poisson loss model. Preprint, 2006.

[54]   Di Graziano C.Rogers. A dynamic approach to the modelling of credit derivatives using markov chains. Preprint, 2006.

[55]   J.BARRAQUAND D.MARTINEAU. Numerical valuation of high dimensional multivariate american securieties. J.Of Finance and Quantitative Analysis, 30:383–405, 1995.

[56]   J.-C. Duan and J.-G. Simonato. Empirical martingale simulation of asset prices. Manangement Science, 44-9:1218–1233, 1998.

[57]   F. Dubois and T. LeliŔvre. Efficient pricing of Asian options by the PDE, approach. Journal of Computational Finance, 10(2), 2006.

[58]   E.Alos. A generalization of the hull and white formula with applications to option pricing approximation. Finance and Stochastics, 10-3:353–365, 2006.

[59]   E.Derman and I. Kani. Riding on a smile. Risk magazine.

[60]   D.Lamberton E.DIA. Monte carlo for pricing asian options in jump models. Preprint, 2010.

[61]   E.Eberlein F.Ozkan. The levy libor model. Finance & Stochastics, IX:327–348, 2005.

[62]   C.Labart E.Gobet. Proceeding de la conf├Č┬ľrence iciam (z├Č┬ijrich, juillet 2007), 2 pages. A sequential Monte Carlo algorithm for solving BSDE., 2007.

[63]   L.C.G.ROGERS E.J.STAPLETON. Fast accurate binomial pricing. preprint, 1997.

[64]   E.LEVY. Pricing european average rate currency options. J.Of International Money and Finance, 11:474–491, 1992.

[65]   Benhamou Eric Gobet Emmanuel and Miri Mohammed. Time dependent heston model. SIAM J. Financial Math., 1:289ÔĂŞ325.

[66]   Benhamou Eric Gobet Emmanuel and Miri Mohammed. Analytical formulas for local volatility model with stochastic rates. Quantitative Finance, to appear, 2011.

[67]   Goldberg Errais, Giesecke. Pricing credit from the top down with affine point processes. Technical report, Preprint, 2007.

[68]   F.A.LONGSTAFF E.S.SCHWARTZ. Valuing american options by simulations:a simple least-squares approach. Working Paper Anderson Graduate School of Management University of California, 25, 1998.

[69]   M.J.BRENNAN E.S.SCHWARTZ. The valuation of the American put option. J. of Finance, 32:449–462, 1977.

[70]   N.JACKSON E.SULI. Adaptive finite element solution of 1d european option pricing problems. Technical Report 5, Oxford Computing Laboratory, 1997.

[71]   E. FOURNIE J.M.LASRY et al. An application of malliavin calculs to montecarlo methods in finance. working paper, 1997.

[72]   E.TEMAM. Monte carlo methods for asian options. preprint, 98-144 CERMICS, 1998.

[73]   C.W. Oosterlee F. Fang. A fourier-based valuation method for bermudan and barrier options under heston’s model. SIAM, 31:826–848, 2008.

[74]   C.W. Oosterlee F. Fang. Pricing early-exercise and discrete barrier options by fourier-cosine series expansions. Numerische Mathematik, 114:27–62, 2009.

[75]   C.W. Oosterlee F. Fang. A novel option pricing method based on fourier-cosine series expansions. Siam J. Finan. Math., 2:439–463, 2011.

[76]   F. Mercurio and D. Brigo. Lognormal-mixture dynammics and calibration to market smiles. Preprint, 2001.

[77]   F.Black and P.Karasinski. Bond and option pricing when short rates are lognormal. Financial Analyst Journal, Juli-August:52–59, 1991.

[78]   L. Feng and V. Linetsky. Computing exponential moments of the discrete maximum of a levy process and look-back options. Journal of Computational Finance, 13(4):501–529, 2009.

[79]   F.Jamshidian. Bond,futures and option evaluation in the quadratric interest rate model. Applied Mathematical Finance, 3:93–115, 1996.

[80]   A Forde, M. Jaquier. Robust approximations for pricing asian options and volatility swaps under stochastic volatility. Applied Mathematical Finance, 17(3), 2010.

[81]   M. Jaquier A Forde. Small-time asymptotics for implied volatility under the heston model. International Journal of Theoretical and Applied Finance, 12(6), 2009.

[82]   M. Jaquier A Mijatovic A. Forde. Asymptotic formulae for implied volatility under the heston model. Proc. R. Soc, 466(2124):3593–3620, 2010.

[83]   R. Carmona J.P. Fouque and D. Vesta. Interacting particle systems for the computation of rare credit portfolio losses. Finance and Stochastics, 13(4), 2009.

[84]   R. Frey and J. Backhaus. Dynamic hedging of synthetic cdo-tranches with spread-and contagion risk. Technical report, Preprint, department of mathematics, Universit├Č┬ďt Leipzig, 2008.

[85]   Paul Glasserman and Kyoung-Kuk Kim. Gamma expansion of the heston stochastic volatility model. Finance and Stochastics, pages 1–30, 2009.

[86]   Paul Glasserman and Kyoung-Kuk Kim. Saddlepoint approximations for affine jump-diffusion models. Journal of Economic Dynamics and Control, 33:37–52, 2009.

[87]   Goute, S. Oudjane N. Russo F. Variance optimal hedging for processes with independent increments and applications. applications to electricity market. Preprint, 2010.

[88]   G.Pages, J.Printems. Functional quantization for numerics with an application to option pricing. Monte Carlo Methods and its Applications, to appear.

[89]   P.BJERKSUND G.STENSLAND. Closed form aproximation of american options prices. to appear in Scandinavian Journal of Management, 1992. Working Paper Norwegian School of Economics and Business Administration.

[90]   H.Buhler. Consistent variance curve models. Finance and Stochastics, 10-2, 2006.

[91]   H.FAURE. DiscrÚpance de suites associÚes Ó un systŔme de numÚration (en dimension s). Acta Arithmetica, XLI:337–361, 1982.

[92]   H.JOHNSON. Options on the maximum ot the minimum of several assets. J.Of Finance and Quantitative Analysis, 22:227–283, 1987.

[93]   D.BUNCH H.JOHNSON. A simple and numerically efficient valuation method for american puts using a modified geske-johnsohn approach. J.of Finance, 47:809–816, 1992.

[94]   H.NIEDERREITER. Points sets ans sequences with small discrepancy. Monatsh.Math, 104:273–337, 1987.

[95]   E.DERMAN I.KANI D.ERGENER I.BARDHAN. Enhanced numerical methods for options with barriers. Financial Analyst Journal, pages 65–74, Nov-Dec 95 1995.

[96]   I.M.SOBOL. The distribution of points in a cube and the approximate evaluation of integrals. U.S.S.R. Computational Math.and Math.Phys., 7(4):86–112, 1967.

[97]   Kolodko A. Schoenmakers J. Iterative construction of the optimal bermudan stopping time. Finance Stoch., 10:27–49, 2006.

[98]   J. Kennedy, P. Hunt A. Pelsser. Markov-functional interest rate models. Finance & Stochastics, 4:391–408, 2000.

[99]   L. ANDERSEN J.ANDREASEN. Volatility smile fitting and numerical methods for pricing. preprint, 1999.

[100]   R. C.Source J.B. C. Van Ginderen, H. Garcia. On the pricing of credit spread options: A two factor hw?bk algorithm. Int. J. Theor. and Appl. Finance, 6-5:491, 2003.

[101]   J.BARRAQUAND. Numerical valuation of high dimensional multivariate european securities. Manangement Science, pages 1882–1891, 1995.

[102]   J.BUSCA. A finite element method for the valuation of american options. Technical report, C.A.R. Internal Report, 1998.

[103]   M.BROADIE J.DETEMPLE. American option valuation : new bounds, approximations and a comparison of existing methods. Review of financial studies, to appear, 1995.

[104]   J.E.ZHANG. A semy-analtycal method for pricing and hedging continously-sampled arithmetic average rate options. preprint, September 2000.

[105]   M S. Joshi J.H. Chan. Fast and accurate long stepping simulation of the heston stochastic volatility model. Preprint, 2011.

[106]   J.H.HALTON. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math., 2:84–90 et erratum, 1960.

[107]   J.Hull and A.WHITE. Valuing derivative securities using the explicit finite difference method. Journal of Financial and Quantitative Analysis, 25:87–100, 1990.

[108]   J.Hull and A.WHITE. Numerical procedures for implementing term structure models ii:two-factor models. The Journal of Derivatives, 2:37–48, 1994.

[109]   J.Hull and A.WHITE. Numerical procedures for implementing term structure models i:single factor models. The Journal of Derivatives, 2:7–16, 1994.

[110]   J.Hull and A.WHITE. Valuing credit derivatives using an implied copula approach. The Journal of Derivatives, 14(2):8–28, 2006.

[111]   J.Hull A.White. Valuation of a cdo and an nth to default cds without monte carlo simulation. The Journal of Derivatives, 2:8–23, 2004.

[112]   Benjamin Jourdain and Mohamed Sbai. Exact retrospective Monte Carlo computation of arithmetic average Asian options. Monte Carlo Methods Appl., 13(2):135–171, 2007.

[113]   Benjamin Jourdain and Mohamed Sbai. High order discretization schemes for stochastic volatility models. Quantitative Finance, to appear, 2011.

[114]   J.P.Laurent J.Gregory. Basket default swaps, cdo’s and factor copulas. preprint.

[115]   D.W.PEACEMAN-H.H.RACHFORD Jr. The numerical solution of parabolic and elliptic differential equations. J.of Siam, 3:28–42, 1955.

[116]   Jr J.DOUGLAS H.H.RACHFORD Jr. On the numerical solution of heat conduction problems in two and tree-space variables. Trans Amer.Math.Soc., 82:421–439, 1956.

[117]   J.Schoenmakers. Calibration of libor models to caps and swaptions: a way around intrinsic instabilities via parsimonious structures and a collateral market criterion. Preprint, 2003.

[118]   J.Schoenmakers. Iterating cancelable snowballs and related exotics in a many-factor libor model. Risk, September, 2006.

[119]   C.Cuchiero M. Keller-Ressel J.Teichmann. Polynomial processes and their applications to mathematical finance. Technical report, Preprint arXiv/0812.4740, 2008.

[120]   J.Teichmann C.Bayer. Cubature on wiener space in infinite dimension. finite difference methods for spdes and hjm-equations. Preprint: arXiv:0712.3763v1, 2008.

[121]   Julian Guyon. Volatilit├Č┬ľ stochastique : ├Č┬ľtude d’un mod├Č┬ĺle ergodique. notes de cours de M2 de Nicole El Karoui, "Mod├Č┬ĺles stochastiques en finance", chapitre "Volatilit├Č┬ľ stochastique", Universit├Č┬ľ Paris V.

[122]   J.Zhu. A simple and exact simulation approach to heston model. Preprint, 2008.

[123]   K.Barty, J.S.Roy, C.Strugarek. Temporal difference learning with kernels for pricing american style options. Preprint, 2005.

[124]   A. Papapantoleon Keller-Ressel M. and J. Teichmann. A new approach to libor modeling. Preprint, arXiv/0904.0555, 2009.

[125]   A.G.Z KEMNA and A.C.F.VORST. A pricing method for options based on average asset values. J. Banking Finan., pages 113–129, March 1990.

[126]   Duffie Darrel Pan Jun Singleton Kenneth. Transform analysis and asset pricing for affine jump-diffusions. Econometrica, pages 1343–1376, 68 2000.

[127]   El Khatib and N. Privault. Computations of greeks in a market with jumps via the malliavin calculus. Finance and Stochastics, to appear, 2003.

[128]   S. G. Kou and H. Wang. First passage times of a jump diffusion process. Adv. Appl. Prob., 35:504–531, 2003.

[129]   S. G. Kou and H. Wang. Option pricing under a double exponential jump diffusion model. Management Science, 50(9):1178–1192, 2004.

[130]   S.TURNBULL WAKEMAN L. A quick algorithm for pricing european average options. J.Of Financial and Quantitative Analysis, 26:377–389, 1991.

[131]   L. Andersen and J. Andreasen. Jump-diffusion processes: Volatility smile fitting and numerical methods for pricing. Preprint, 1 999.

[132]   L. Kaisajuntti, J. Kennedy. An n-dimensional markov-functional interest rate mode. Preprint, 2008.

[133]   L.Andersen. Volatility skews and extension of the libor market models. Applied Mathematical Finance, 7:1–32, 2000.

[134]   L.Andersen. Simple and efficient simulation of the heston stochastic volatility models. Journal of Computational Finance, 11-3, 2008.

[135]   L.Andersen J.Sidenious. Extension to the gaussian copula: Random recovery and random factor loadings. preprint.

[136]   H.Ben Hameur M.Breton P. L’Ecuyer. A numerical procedure for pricing american-style asian option. preprint, 1999.

[137]   REGNIER H. LIONS P.L. Calcul du prix et des sensibilites d’une option americaine par une methode de monte-carlo. Technical report, Preprint, 2000.

[138]   L.MACMILLAN. Analytic approximation for the American put option. Advances in Futures and Options Research, 1:119–139, 1986.

[139]   P. CARR L.Wu. Static hedging of standard options. Technical report, preprint, 2003.

[140]   B.M.GOLDMAN H.B.SOSIN M.A.GATTO. Path dependent options: buy at low, sell at high. J. of Finance, 34:111–127, 1979.

[141]   Maller-Solomon-Szymaier. A multinomial approximation for american option price in levy process models. Mathematical finance, 16-4:589–694, 2006.

[142]   Carr Peter Geman Helyette Madan Dilip B. Yor Marc. Option valuation using the fast fourier transform. Math. Finance, 13(3):345–382, 2003.

[143]   M.Attari. Option pricing using fourier transforms: A numerically efficient simplification. Technical report, Preprint, 2004.

[144]   M.Avellaneda, C. Friedman, R. Buff, and N. Granchamp. Weighted monte-carlo: A new technique for calibrating asset-pricing models. Int. J. Theor. and Appl. Finance, 4(1):>91–119, 2001.

[145]   M.Avellaneda, C. Friedman, R. Holmes, and D. Samperi. Calibrating volatility surfaces via relative entropy minimization. Appl. Math. Finance, 4:37–64, 1997.

[146]   M.B. Pedersen. Bermudan swaptions in the libor market model. SimCorp Financial Research Working Paper, 1999.

[147]   L.Andersen M.Broadie. Primal-dual simulation algorithm for pricing multidimensional american options. Manangement Science, 50-9:1222–1234, 2004.

[148]   M.Broadie M.Cao. Improved lower and upper bound algorithm for pricing american options by simulation. Quant. Finance, 8-8:845–861, 2008.

[149]   M.Costabile M.Gaudenzi I.Massabo A Zanette. Evaluating fair premiums of equity-linked policies with surrender option in a bivariate model. Insurance Math. Econom, 45-2, 2009.

[150]   M.Gaudenzi A Zanette. Pricing american barrier options with discrete dividends by binomial trees. Decis. Econ. Finance, 32, 2009.

[151]   M.Gaudenzi M.A.Lepellere A Zanette. The singular points binomial method for pricing american path-dependent options. J. Comput. Finance, 14, 2010.

[152]   M.Giles. Multi-level monte carlo path simulation. Operations Research, 56-3:607–617, 2008.

[153]   P.BALDI L.CARAMELLINO M.G.IOVINO. Pricing single and double barrier options via sharp large deviations. Preprint, 1997.

[154]   M.H.Vellekoop J.V.Nieuwenhuis. Efficient pricing of derivatives on assets with discrete dividends. Applied Mathematical Finance, 13-3:265–284, 2006.

[155]   G.Fusai D.Marazzina M.Marena. Pricing fixed and floating asian options in a discretely monitored framewor. SIAM J. Financial Math, 2:383–403, 2011.

[156]   M.Ninomiya and S.Ninomiya. A new higher-order weak approximation scheme for stochastic differential equations and the runge├ć┬Ă┬Şkutta method. Finance & Stochastics, 13-3, 2009.

[157]   G.BARLES C.DAHER M.ROMANO. Convergence of numerical schemes for problems arising in finance theory. Math. Models and Meth. in Appl. Sciences, 5:125–143, 1995.

[158]   M.RUBINSTEIN. Return to oz. Risk, 7(11):67–71, 1994.

[159]   E.REINER M.RUBINSTEIN. Breaking down the barriers. Risk, 4:28–35, 191.

[160]   J.COX S.ROSS M.RUBINSTEIN. Option pricing: a simplified approach. J. of Economics, January 1978.

[161]   F.BLACK M.SCHOLES. The pricing of Options and Corporate Liabilities. Journal of Political Economy, 81:635–654, 1973.

[162]   Y.SAAD M.SCHULTZ. Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear sytems. SIAM J. Sci. Static.Comput., 7:856–869, 1986.

[163]   H.GEMAN M.YOR. Pricing and hedging double barrier options: a probabilistic approach. Mathematical finance, 6:365–378, 1996.

[164]   S.Levendorskiy N.Boyarchenko. The eigenfunction expansion method in multi-factor quadratic term structure models. Mathematical finance, 17-4:509–539, 2006.

[165]   N.El Karoui J.Jiao. Approximation of large portfolio losses by stein’s method and zero bias transformation. Preprint, 2006.

[166]   N.KUNIMOTO N.IKEDA. Pricing options with curved boundaries. Mathematical finance, 2:275–298, 1992.

[167]   N.Jackson, E.SŘli, and S. Howison. Computation of deterministic volatility surfaces. Journal Computational Finance, 2(2), 1999.

[168]   N.J.NEWTON. Variance reduction for simulated diffusions. SIAM J. Appl. Math., 54(6):1780–1805, 1994.

[169]   N.JU. Pricing an american option by approximating its early exercise boundary as a multipiece exponential function. The Review of Financial Studies, 11, 3:627–646, 1998.

[170]   N.Moreni. Pricing american options:a variance reduction technique for the longstaff-schwartz algorithm. Technical report, Cermics, 2003.

[171]   N.Moreni. Methodes de monte carlo et valorisation d’options. Phd Thesis, 2005.

[172]   F.Mercurio N.Moreni. Pricing inflation indexed options with stochastics volatility. Preprint, 2006.

[173]   M.Broadie O.Kaya. 2004 winter simulation conference (wsc’04)). Exact Simulation of Option Greeks under Stochastic Volatility and Jump Diffusion Models, 2:535–543, 2004.

[174]   S.Levendroskii O.Kudrayavtsev. Fast pricing of american and barrier options under levy processes. preprint available at SSRN:

[175]   Lech A. Grzelak Cornelis W. Oosterlee. On the heston model with stochastic interest rates. Preprint, 2010.

[176]   A. Papapantoleon, J. Schoenmakers, and D. Skovmand. On efficient and accurate log-LÚvy approximations for LÚvy-driven LIBOR models. Preprint, TU Berlin, 2011.

[177]   P.Carr G.Yang. Simulating bermudan interest rate derivatives. Working Paper Morgan Stanley, 1998.

[178]   P.Carr R.Lee. Realized volatility and variance: Options via swap. Risk magazine, May 2007.

[179]   P.Collin-Dufresne and R.S. Goldstein. Pricing swaoptions within an affine framework. The Journal of Derivatives, Fall:1–18, 2002.

[180]   P.Etore E.Gobet. Stochastic expansion for the pricing of call options with discrete dividends. Applied Mathematical Finance, to appear, 2012.

[181]   M.BROADIE P.GLASSERMANN. Pricing american-style securities using simulation. J.of Economic Dynamics and Control, 21:1323–1352, 1997.

[182]   M.BROADIE P.GLASSERMANN. A stochastic mesh method for pricing high-dimensional american options. Working Paper, Columbia University:1–37, 1997.

[183]   P.Glassermann N.Merener. Numerical solution of jump-diffusion libor market models. Finance and Stochastics, 7:1–27, 2003.

[184]   P.Glassermann X.Zhao. Arbitrage-free discreitzation of lognormal libor and swap rate models. Finance and Stochastics, 4:35–68, 2000.

[185]   P.Glassermann X.Zhao. Fast greeks by simulation of forward libor models. Journal of Computational Finance, 3-1:5–39, 2000.

[186]   P.Glassermann Z.Liu. Estimating greeks in simulating levy-driven models. Journal of Computational Finance, 14-2, 2010.

[187]   P.J.Schonbucher. A tree implementation of a credit spread model for credit derivatives. Journal of Computational Finance, 6-2, 2002.

[188]   P.RITCHKEN. On pricing barrier options. Journal Of Derivatives, pages 19–28, Winter 95 1995.

[189]   B.KAMRAD P.RITCHKEN. Multinomial approximating models for options with k state variables. Management Science, 37:1640–1652, 1991.

[190]   P.GLASSERMAN P.HEIDELBERGER P.SHAHABUDDIN. Gaussian importance sampling and stratification computational issue. Computer Science/Mathematics, September, 1998.

[191]   P.GLASSERMAN P.HEIDELBERGER P.SHAHABUDDIN. Asymptotically optimal importance sampling and stratification for prcing path-dependent options. Mathematical Finance, 2,April:117–152, 1999.

[192]   R. Cont and A.Minca. Recovering portfolio default intensities implied by cdo quotes. To appear in Mathematical Finance, 2008.

[193]   R. Cont and E. Voltchkova. A finite difference scheme for option pricing in jump diffusion and exponential lÚvy models. SIAM Journal on Numerical Analysis, 43(4):1596–1626, 2005.

[194]   S. Jaimungal R. Jackson and V. Surkov. Fourier space time-stepping for option pricing with levy models. Journal of Computational Finance, 12-2, 2008.

[195]   R.Bahr C.Chiarella N.El-Hassan X.Zheng. The reduction of forward rate volatility hjm models to markovian form: pricing european bond options. Journal of Computational Finance, 3-3:47–72, 2000.

[196]   R.BREEN. The accelerated binomial option pricing. J.Of Finance and Quantitative Analysis, 26:153–164, 1991.

[197]   L.Andersen R.Brotherton-Ratcliffe. Extended libor market models with stochastic volatility. Journal of Computational Finance, 9(1), 2005.

[198]   L.ANDERSON R.BROTHERTON-RATCLIFFE. Exact exotics. Risk, 9:85–89, Oct 1996.

[199]   R.Carmona N.Touzi. Optimal multiple stopping and valuation of swing options. preprint.

[200]   R.C.MERTON. Option pricing when the underlying stocks returns are discontinuous. Journ. Financ. Econ., 5:125–144, 1976.

[201]   R.D.Smith. An almost exact simulation method for the heston model. Journal of Computational Finance, 11-1, 2007.

[202]   G.BARONE-ADESI R.E.WHALEY. Efficient analytic approximation of American option values. Journal of Finance, 42:301–320, 1987.

[203]   R.Lagnado and S. Osher. A technique for calibrating derivative security pricing models: numerical solution of an inverse problem. J. Comp. Fin., 1(1):13–25, 1997.

[204]   R.Lord. Partially exact and bounded approximations for arithmetic asian options. Journal of Computational Finance, 10-2, 2006.

[205]   R.Lord C.Kahl. Optimal fourier inversion in semi-analytical option pricing. Journal of Computational Finance, 10-4, 2007.

[206]   R.Lord, R.Koekkoek, D.J.C.Van Dijk. A comparison of biased simulation schemes for stochastic volatility models. Preprint, 2006.

[207]   L.C.G. Rogers. Montecarlo valuation of american option. Preprint, 2000.

[208]   J.N.TSITSIKLIS B.VAN ROY. Optimal stopping of markov processes: Hilbert spaces theory, approximations algorithms and an application to pricing high-dimensional financial derivatives. IEEE Transactions on Automatic Control, 44(10):1840–1851, October 1999.

[209]   J.N.TSITSIKLIS B.VAN ROY. Regression methods for pricing complex american-style options. Working Paper, MIT:1–22, 2000.

[210]   R.STULZ. Options on the minimum or the maximum of two risky assets. J. of Finance, 10:161–185, 1992.

[211]   A.CONZE R.VISWANATHAN. Path dependent options: the case of lookback options. J. of Finance, 46:1893–1907, 1992.

[212]   S.BABBS. Binomial valuation of lookback options. working paper,Midland Global Markets London, 1992.

[213]   Schonbucher. Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives. Preprint, 2005.

[214]   M.A.MILEVSKY S.E.POSNER. Asian options,the sum of lognormals and the reciprocal gamma distribution. J.Of Financial and Quantitative Analysis, 3:409–422, September 1998.

[215]   S.FIGLEWSKI-B:GAO. The adaptive mesh model:a new approach to efficient option pricing. Journal of Financial Economics, 53:331–351, 1999.

[216]   P.BOYLE J.EVNINE S.GIBBS. Numerical evaluation of multivariate contingent claims. Review of Financial Studies, 2:241–250, 1989.

[217]   M.BROADIE P.GLASSERMANN S.KOU. A continuity correction for discrete barrier options. Mathematical Finance, 7, 1997.

[218]   O.Kudryavtsev S.Levendorskiy. Fast pricing of american and barrier options under levy processes. Preprint, 2007.

[219]   S.L.HESTON. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6(2):327–343, 1993.

[220]   S.M. Ould Aly. Forward variance dynamics : Bergomi’s model revisited. Preprint hal-00624812.

[221]   S.M. Ould Aly. Option pricing for a lognormal stochastic volatility model. Preprint hal-00623935.

[222]   S.M.T.Ehrlichman S.G.Henderson. Adaptive control variates for pricing multi-dimensional american options. Journal of Computational Finance, 11-1, 2007.

[223]   S.Ninomiya N.Victoir. Weak approximation and derivative pricing. Preprint, 2005.

[224]   P. Tankov. Processes in Finance: Inverse Problems and Dependence Modelling. PhD thesis, Ecole Polytechnique, 2004.

[225]   G.W.P. THOMPSON. Fast narrow bounds on the value of asian options. Working paper Judge Institute U. of Cambridge, 1999.

[226]    J.BARRAQUAND T.PUDET. The pricing of american path-dependent contingent claims. Mathematical Finance, 6(1):17–51, 1996.

[227]   T.S.HO-R.C.STAPLETON-M.G.SUBRAHMANYAM. A simple technique for the valuation and hedging of american options. The Journal of Derivatives, pages 52–66, Fall 1994.

[228]   T.CHEUK T.VORST. Lookback options and the observation frequency. working paper,Erasmus University Rotterdam, 1994.

[229]   T.CHEUK T.VORST. Complex barrier options. Journal of Derivatives, 4:8–22, 1996.

[230]   G.PAGES V.BALLY. A quantization method for the discretization of bsde’s and reflected bsde’s. Working Paper UniversitÚ Paris XII, pages 1–40, 2000.

[231]   V.Bally E.Temam. Empirical semi-groups and calibration. Preprint, 2004.

[232]   R.Carmona V.Durlemann. Generalizing the black-scholes formula to multivariate contingent claims. Journal of Computational Finance, 9(2), 2005.

[233]   L.C.G. Rogers L.A.M. Veraart. A stochastic volatility alternative to sabr. J. Appl. Probab., 45(4):1071–1085, 2008.

[234]   Eberlein R.Frey E. A. von Hammerstein. Advanced credit portfolio modeling and cdo pricing. In Springer, editor, in Mathematics ├ć┬Ă┬Ş Key Technology for the Future, W. J├Č┬ďger, and H.-J. Krebs, (Eds.),, pages 253–280, 2008.

[235]   H.VAN DER VORST. Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM J. Sci. Static.Comput., 13:631–644, 1992.

[236]   V.Piterbarg. A stochastic volatility forward libor model with a term structure of volatility smiles. Preprint.

[237]   V.Piterbarg. Pricing and hedging callable libor exotics in forward libor models. Journal of Computational Finance, 8-2, 2005.

[238]   S.Levendroskii O.Kudrayavtsev V.Zherder. The relative efficency of numerical methods for pricing american options under levy procecess. Journal of Computational Finance, 9(2), Winter 2005-2006.

[239]   Wang, Y., Caflisch, R. Pricing and hedging american-style options: A simple simulation-based approach. Journal of Computational Finance, 13-4, 2010.

[240]   W.HACKBUSCH and U.TROTTENBERG, editors. Multigrid Methods, volume 960 of Lecture Notes in Math. Springer Verlag, 1981.

[241]   H.A. Windcliff, P.A. Forsyth, and K.R. Vetzal. Numerical methods and volatility models for valuing cliquet options. Applied Mathematical Finance, 13, 2006.

[242]   W.M.Schmidt. On a general class of one-factor models for the term structure of interest rat. Finance & Stochastics, 1:3–24, 1997.

[243]   W.WAGNER. Monte carlo evaluation of functionals of stochastic differential equations—variance reduction and numerical examples. Stoch. Analysis Appl., 6:447–468, 1988.

[244]   X.Burtschell J.P.Laurent J.Gregory. A comparative analysis of cdo pricing models. preprint.

[245]   J.Yang T.R.Hurd X.Zhang. Saddlepoint approximation method for pricing cdos. Journal of Computational Finance, 8(2):1–20, 2006.

[246]   Y. Achdou and O. Pironneau. A numerical procedure for the calibration of volatility with American options. Applied Mathematical Finance, to appear, 2005.

[247]   Y.Tang J.Lang. A nonexploding bushy tree technique and its application to the multifactor interest rate market model. Journal of Computational Finance, 4-4:5–31, 2001.

[248]   X. Zhang. Analyse numÚrique des options amÚricaines dans un modŔle de diffusion avec sauts. Technical report, CERNA-Ecole Nationale des Ponts et ChaussÚes, 94.

[249]   L.C.G.ROGERS Z.SHI. The value of an asian option. J. Appl. Probab., 32(4):1077–1088, 1995.