Pricing and hedging short-maturity Asian options in local volatility models
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| Format: | Preprint |
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2019
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| _version_ | 1866917651767361536 |
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| author | Kim, Jaehyun Park, Hyungbin Park, Jonghwa |
| author_facet | Kim, Jaehyun Park, Hyungbin Park, Jonghwa |
| contents | This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a Hölder continuous payoff function in a local volatility model. The main idea of this analysis is that the local volatility model can be approximated by a Gaussian process at short maturity $T.$ By combining this approximation argument with Malliavin calculus, we conclude that the short-maturity behaviors of Asian option prices and the delta values are approximately expressed as those of their European counterparts with volatility $$σ_{A}(T):=\sqrt{\frac{1}{T^3}\int_0^Tσ^2(t,S_0)(T-t)^2\,dt}\,,$$ where $σ(\cdot,\cdot)$ is the local volatility function and $S_0$ is the initial value of the stock. In addition, we show that the convergence rate of the approximation is determined by the Hölder exponent of the payoff function. Finally, the short-maturity asymptotics of Asian call and put options are discussed from the viewpoint of the large deviation principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_12944 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Pricing and hedging short-maturity Asian options in local volatility models Kim, Jaehyun Park, Hyungbin Park, Jonghwa Mathematical Finance This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a Hölder continuous payoff function in a local volatility model. The main idea of this analysis is that the local volatility model can be approximated by a Gaussian process at short maturity $T.$ By combining this approximation argument with Malliavin calculus, we conclude that the short-maturity behaviors of Asian option prices and the delta values are approximately expressed as those of their European counterparts with volatility $$σ_{A}(T):=\sqrt{\frac{1}{T^3}\int_0^Tσ^2(t,S_0)(T-t)^2\,dt}\,,$$ where $σ(\cdot,\cdot)$ is the local volatility function and $S_0$ is the initial value of the stock. In addition, we show that the convergence rate of the approximation is determined by the Hölder exponent of the payoff function. Finally, the short-maturity asymptotics of Asian call and put options are discussed from the viewpoint of the large deviation principle. |
| title | Pricing and hedging short-maturity Asian options in local volatility models |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/1911.12944 |