| Title | Hedging barrier options through a log-normal local stochastic volatility model |
| Creator | |
| Date Issued | 2017 |
| Source Publication | Proceedings - 22nd International Congress on Modelling and Simulation, MODSIM 2017
 |
| Pages | 770-776 |
| Abstract | In the equity and foreign exchange (FX) markets, there has been a shift towards using non-affine pricing models as these have been shown to produce more realistic volatility distributions and more accurately capture market dynamics. One such non-affine model is the Inverse Gamma model, which we have incorporated into a Local-Stochastic Volatility (LSV) model termed the Log-normal-LSV (LN-LSV) that can, once calibrated, accurately reproduce market prices of exotic options Langrene and Zhu [2016]. The LN-LSV model is a non-parametric combination of local volatility and stochastic volatility models, in which both the spot price and stochastic volatility follow log-normal processes. The LN-LSV model is calibrated using both the market-traded implied volatility surface and market exotic option prices. However, while the accurate pricing of exotic options is necessary for good pricing model performance, it is also necessary for models to perform in risk management applications, where hedges are entered into to minimise risk. Therefore, the accurate calculation of the derivatives of the option price with respect to the asset or volatility (the Greeks) is also necessary for good model performance. This paper aims to characterise the hedging performance of the Log-normal Local-Stochastic Volatility model for a variety of hedging instruments using an historical dataset consisting of daily spots and volatility surfaces for the EUR/USD market over a five-year time period. We use delta-gamma hedging for different barrier options under the LN-LSV model and compare the hedging performance with that of the Black-Scholes (BS) model. Then we use the numerical results to demonstrate that the LN-LSV model is more effective than the BS model. We use five types of reverse knock-out options as test cases over a time period of five years. On each trading day from 2007 to 2011, the five options are firstly priced using the LN-LSV model. After pricing, each option is hedged daily until the expiry date of the option using a delta-gamma neutral scheme under both the LN-LSV and BS models. To measure the hedging performance, each profit-loss outcome forms one point of the P&L distribution. During Jan 2007 to Dec 2011, the profit and loss of a total of 1100 traded options for each option type forms the P&L distribution. Compared to the Black-Scholes model, the P&L distribution of the numerical results from LN-LSV model is more symmetric and is less likely to have extreme profit-loss outliers. Thus it produces more superior hedging performance. |
| Keyword | Barrier option Black-Scholes model Delta-Gamma hedging Hedging performance Log-Normal Local Stochastic Volatility model |
| URL | View source |
| Language | 英语English |
| Scopus ID | 2-s2.0-85080862115 |
| Citation statistics | |
| Document Type | Conference paper |
| Identifier | http://repository.uic.edu.cn/handle/39GCC9TT/9655 |
| Collection | Research outside affiliated institution |
| Corresponding Author | Lee，G. |
| Affiliation | CSIRO DATA61-Real Options and Financial Risk,Clayton,3168,Australia |
| Recommended Citation GB/T 7714 | Ning，Wei,Lee，G.,Langrene，N. Hedging barrier options through a log-normal local stochastic volatility model[C], 2017: 770-776. |
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