Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

Abstract

W e obtain a closed-form solution for pricing European options under a general jump-diffusion model that can incorporate arbitrary discrete jump-size distributions, including nonparametric distributions such as an empirical distribution. The flexibility in the jump-size distribution allows the model to better capture leptokurtic features found in real-world data. The model uses a discrete-time framework and leads to a pricing formula that is provably convergent to the continuous-time price as the discretization is increased. The solution is easy to implement with fast convergence properties. Numerical results illustrate the efficiency and accuracy of the proposed model and highlight its robustness and flexibility.

Option pricing under a discrete-time Markov switching stochastic volatility with co-jump model

“…Thus, given the probability distribution {p V (•)}, the option price only depends on C jd (•). When ln(J t ) follows a normal distribution, a mixed-exponential distribution, or a general discrete distribution, C jd (•) can be obtained via various approaches, such as [51], [43], [44], [15] and [32]. Hence, under the MS-SVJ model with the above jump size distribution, we also provide an analytical solution for the option price.…”

Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model

“…Thus, given the probability distribution {p V (•)}, the option price only depends on C jd (•). When ln(J t ) follows a normal distribution, a mixed-exponential distribution, or a general discrete distribution, C jd (•) can be obtained via various approaches, such as Merton (1976), Kou (2002), Kou and Wang (2004), Cai and Kou (2011), or Fu et al (2017). Hence, under the MS-SVJ model with the above jump size distribution, we also provide an analytical solution for the option price.…”

Optimal unbiased estimation for expected cumulative discounted cost

“…In the following, we consider the exponential Lévy process, which includes geometric Brownian motion (GBM) as a special case; see e.g. Fu et al (2017). Let Y t be a Lévy process with the characteristic triplet (µ, σ 2 , ν), and its characteristic exponent is given by φ(•), which is uniquely characterized by the Lévy-Khintchine formula: E[e βYt ] = e tφ(β) .…”