Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility

Abstract

Please cite this article as: Y. Xing, X. Yang, Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility, Journal of Computational and Applied Mathematics (2014), http://dx. AbstractIn this paper, we continue to investigate the model related to Bakshi and Chen (1997). In our model, both of the money supplies in the two countries are assumed to follow jump-diffusion processes with stochastic volatility. In the set of the two-country economy, we obtain the equilibrium price of the nominal exchange rate. With the help of Fourier transform to solve a partial integro-differential equation (PIDE), we get a closedform solution to the PIDE for a European call currency option. We also do Monte Carlo simulations to verify the correctness of the derived formula. Our model contains some existing currency option models as special cases, for example the stochastic-volatility jumpdiffusion (SVJD) model in Bates(1996), in which the jump of the exchange rate is driven by one Poisson process. We also provide some numerical analysis to show that our model is effective to the foreign currency option market.

Equilibrium Valuation of Currency Options Under a Discontinuous Model With Co-Jumps

“…If the problem (4) exists a solution under the above three assumptions, an equilibrium price is obtained. Applying the dynamic stochastic programming method, we can obtain the prices of a nominal exchange rate and a zero-coupon bond at time t. For the proof details, see [22].…”

“…They obtained closed-form solutions for foreign exchange claims following the two-country economy assumption. Then, based on the Bakshi and Chen [1] model, Xing and Yang [22] priced the equilibrium currency option prices under a jumpdiffusion model with stochastic volatility. However, the jump parts of the money supplies in the domestic and foreign country were assumed mutually independent and the jump intensities were both constants, which was not very consistent with the real market.…”

Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

“…In different environments, such as bull markets or bear markets, the returns of stock prices have different properties and distributions to follow, based on which many different models (see [1][2][3][4][5][6][7]) are proposed and some analytic formulae or approximations are provided. For some classical models without analytic solutions, lots of efficient numerical methods (see [8][9][10][11][12][13][14]) are presented in detail. In addition, by employing some existing model and numerical methods, some researches (see [15,16]) focus on the empirical tests on actual data, and some great findings are observed in the real derivative markets.…”

Equilibrium valuation of currency options with stochastic volatility and systemic co-jumps

“…Following the two-country economy assumption, [2] constructed a stochastic volatility model and obtained a closed form solution for a European currency option. Based on the model in [2], the money supplies were assumed to follow jump-diffusion processes with stochastic volatility in [33]. [9] considered a small open economy and obtained a closed form formula of the currency option under a jump diffusion model.…”

“…When there are jumps in the money supplies in the two-country economy, the following results in equilibrium can be derived. More details can be refer to [33].…”