A delay financial model with stochastic volatility; martingale method |
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Authors: | Min-Ku LeeJeong-Hoon Kim Joocheol Kim |
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Affiliation: | a Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Koreab Department of Economics, Yonsei University, Seoul 120-749, Republic of Korea |
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Abstract: | In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under this hybrid model. The core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term. Subsequently, a correction effect on the European option price is demonstrated both theoretically and numerically for a good agreement with practical results. |
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Keywords: | Black-Scholes formula Delay Stochastic volatility Martingale Option pricing |
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