Accepting the classic Black-Scholes model for a financial market consisting of a riskless bank account (Bt)0 t T and a risky stock (St)0 t T , and considering the problem of pricing an option of American type associated with the reward process f = (ft)0 t T , we address and discuss the question of the option risk. Motivated by the basic facts of the option pricing theory in complete markets rev...

In this paper we study the pricing problem of multiple exercise options in continuous time on a finite time horizon. For the corresponding multiple stopping problem, we prove, under quite general assumptions, the existence of the Snell envelope, a reduction principle as nested single stopping problems, and a Doob-Meyer type decomposition for the Snell envelope. The main technical difficulty ari...

Spectral and Cubature Methods in Finance and Econometrics An interdisciplinary international research workshop University of Leicester, UK, June 1820, 2009 Supported by AMAMEF, EPSRC, LMS, Oxford-Man Institute and University of Leicester Organizers Sergei Levendorskiĭ, Dept. of Mathematics, University of Leicester Terry Lyons, Oxford-Man Institute, University of Oxford Martijn Pistorius, Dept. ...

An efficient Monte-Carlo simulation for the pricing of barrier options in a Markov-switching model is presented. Compared to a brute-force approach, relying on the simulation of discretized trajectories, the presented algorithm simulates the underlying stock-price process only at state changes and at maturity. Given these pieces of information, option prices are evaluated using the probability ...

We study the arbitrage free option pricing problem for constant elasticity of variance (CEV) model. To treat the stochastic aspect of the CEV model, we direct attention to the relationship between the CEV model and squared Bessel processes. Then we show the existence of a unique equivalent martingale measure and derive the Cox’s arbitrage free option pricing formula through the properties of sq...

Non-parametric and computational methods of option pricing have recently attracted attention of researchers. These typically include highly data intensive, model-free approaches that complement traditional parametric methods. Non-parametric and computational methods of option pricing typically include highly data intensive, model-free approaches that complement traditional parametric methods. O...

The advantage of Monte Carlo simulations is attributed to the flexibility of their implementation. In spite of their prevalence in finance, we address their efficiency and accuracy in option pricing from the perspective of variance reduction and price convergence. We demonstrate that increasing the number of paths in simulations will increase computational efficiency. Moreover, using a t-test, ...

In this paper, we discuss the problem of pricing one exotic option, the strong path dependent Asian option using the Black–Scholes model and compare how the pricing algorithm can be implemented on Intel® Many Integrated Core or MIC Architecture and achieve impressive performance gains. We can demonstrate that a 2-year contract with 252 times steps and 1,000,000 samples can be priced in approxim...

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. ...

We construct efficient and accurate numerical algorithms for pricing discretely monitored barrier and Bermudan style options under time-changed Lévy processes by applying the fast Hilbert transform method to the log-asset return dimension and quadrature rule to the dimension of log-activity rate of stochastic time change. Some popular stochastic volatility models, like the Heston model, can be ...