Accumulated Foreign Exchange Options Pricing Under G-K Model And MRL Model

As the core of financial derivatives, options pricing theory is an important part of modern finance theory, its role is inestimable.Early in 21st century, accumulator generated in Europe,due to its high leverage,it was banned in Europe and America subsequently.After 2005, the Asian financial market grew strong,acumulator products became very popular in Asian region, especially Hong Kong of China.Accumulated currency option is a kind of derivative financial instruments which trading currency in a form of contractual,usually between the investment bank and the investor.There is no premium, but require investors to prepare assets as collateral.Beacuse of its high leverage, during the US subprime mortgage crisis in 2008,investors suffered heavy losses.When researchers analysis the event,they found that:unreasonable option pricing is one of the reasons which caused losses. Therefore, accumulators’reasonable pricing can make it play an effective role in the financial markets and it’s very important.At present, at home and abroad,researches about the accumulative foreign exchange options pricing are rarely, the existing just assumes that the exchange rate is subject to the B-S model, in fact this assumption is not very reasonable.In 1983,Garman and Kohlhagen modified the B-S model,first put forward the model for currency options pricing clearly, named G-K model.But it has some defects.In the later study,scholars found that there is a mean reversion characteristic of exchange rate price,then they expanded the G-K model,named MRL model.This article assumes that foreign exchange rates are subject to G-K model and MRL model,investigate the accumulated currency options pricing.This article aims to derive accumulated currency options’ price formula under GK model and MRL model,then give Monte Carlo numerical methods for accumulated exchange options’ pricing.Use matlab to programme for numerical simulation. Compare the numerical solution with the theoretical solution and do some analysis. Results show that Monte Carlo have a good approximation,it is suitable for strong path dependent options’ pricing problem. The last, I use several figures of three-dimensional surface to show the accumulated foreign exchange options’ price under different contract period in both models, and give the corresponding reasonable explanation.