We study Dupire’s equation for local volatility models with bubbles. The equation for call options contains extra terms compared to the usual equation, whereas, surprisingly enough, the Dupire equation for put options does not contain any extra terms. We also note that uniqueness of solutions to the Dupire equation is lost in general, and we show how to single out the option price among all pos...

We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. In higher dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal comp...

This paper examines the pricing of options by approximating extensions of the Black{Scholes setup in which volatility follows a separate diiusion process. It generalizes the well{known binomial model, constructing a discrete two{ dimensional lattice. We discuss convergence issues extensively and calculate prices and implied volatilities for European{ and American{style put options. A Deutscher ...

We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. In higher dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal comp...

We discuss the ‘continuity correction’ that should be applied to connect the prices of discretely sampled American put options (i.e. Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we compute the correction and relate it to that discussed by Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) for barrier options. In the Ber...

For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the...

We present an algorithm and its software implementation that computes implied volatilities for exchangetraded stock options. The LR (Leisen-Reimer) binomial tree is used for the underlying option pricing, which is adjusted for dollar cash dividends. The Brent’s method is used as the root-finding procedure. The option pricing procedure that is at the core of the root-finding is optimised to maxi...

This paper extends the model proposed by Papahristodoulou [C. Papahristodoulou, Option strategies with linear programming, European Journal of Operational Research 157 (2004) 246–256] to a multi-asset setting to deal with a portfolio of options and underlying assets. General linear programming model is given and it is applied to Novartis, Sanofi and AstraZeneca’s call and put options. A portfol...

In this paper, we illustrate how to value American-style options using the Least-Squares Monte Carlo (LSM) approach proposed by Longstaff and Schwartz (2001) and investigate whether there exists an optimal regression complexity in the LSM framework for options pricing. In particular, we use the smoothing spline in the regression step, which allows us to control the regression complexity on a co...

We measure asset price jumps by the hedging error they induce on a delta-hedged position of European options. Based on high frequency data, we propose a nonparametric estimator for this measure and a test for its positivity. We further construct a Kolmogorov-type test for the presence of jump hedging errors for a possibly infinite-dimensional family of options based on the worst-case contract i...