On the explicit evaluation of the Geometric Asian options in stochastic volatility models with jumps

Abstract

a b s t r a c tIn the present paper we provide a semiexplicit valuation formula for Geometric Asian options, with fixed and floating strike under continuous monitoring, when the underlying stock price process exhibits both stochastic volatility and jumps. More precisely, we shall work in the Barndorff-Nielsen and Shephard (BNS) model framework. We shall provide some numerical illustrations of the results obtained.

Geometric Asian option pricing in general affine stochastic volatility models with jumps

“…The results agree 1 with those from [HS11], which were obtained by a different technique without employing the general affine framework and Riccati equations.…”

“…In [HS11] a semi-explicit evaluation formula for Geometric Asian Options, for fixed and floating strike, under continuous monitoring, when both stochastic volatility and jumps come into play has been provided; in that paper a specific model framework was considered, i.e. the Barndorff-Nielsen and Shephard model.…”

Convergence in multiscale financial models with non-Gaussian stochastic volatility

“…Proof. The property (21) can be deduced from (20) using a result of Abelian-Tauberian type, see [30,Thm. 10.2].…”

Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate

“…For 2 Complexity this reason, stochastic volatility (hereafter SV) models have been proposed in finance (see Hull and White [13], Stein and Stein [14], Heston [15], and others). These models have been applied to value the Asian options (see, e.g., Wong and Cheung [16], Hubalek and Sgarra [17], Kim and Wee [18], and Shi and Yang [19]). In addition, interest rates are stochastic and stock returns are negatively correlated with interest rate changes, which have been examined in previous research.…”