Pricing Model And Algorithm Of Asian Option

Asian option is one of the most active options in today’s financial derivatives market. Itis a new kind option which derived from the standard option, and has played a very importantrole in equity incentive, the exchange market and the bond market. It’s been a very short timesince Asian option launched to the market, but it has always been researched and concernedby the academics and the industry research. Compared to its importance, its theoreticalresearch is lagging behind, so the study of the Asian option pricing has highly academic valueand important practical significance.Asian options, also known as the average price option, different from the standardEuropean option, is a path-dependent options, and its yield to maturity does not depend on theunderlying asset price of the option expiration date, but depending on the average underlyingasset price within a certain period of time of the option contract period. The study of Asianoption is still in-depth exploration stage, based on the previous studies, this paper considersthe impact of several factors on the Asian option prices, and tries to give the Asian optionpricing methods of numerical simulation based on the Black-Scholes model, and the fuzzy settheory is given a new pricing methods for Asian options to investors for investmentdecision-making reference. This paper studies the Asian option pricing from the followingtwo aspects:Firstly: considering the underlying asset price will always occurred in a discontinuousjump, which impacted by some unexpected events in the reality financial market, this paperassumes that the underlying asset price follows the jump-diffusion process; on the other,empirical studies have shown that the risk-free interest rate in the market is not constant, sothis paper assumes that risk-free interest rate subject to the short-term stochastic interest ratemodel; finally, in order to improve the flexibility of the investment, taking the American-styleAsian option into consideration which can be traded on any one trading day before the duedate, this paper establishes the American-style Asian option pricing model with jumps understochastic interest rate, and proposes a simulation solution algorithm based on the idea ofLongstaff’s least squares Monte Carlo numerical pricing methods. In order to improve theaccuracy and timeliness of the simulation algorithm, this paper uses variance reductiontechniques and low-difference random Faure sequences to improve the random numberaggregation of the Monte Carlo simulation; together, considering that the least squaresregression is not comprehensive (only considers independent variable), this paper uses thetotal least squares regression alternative to obtain the more accurate results. Finally, the quasi-Monte Carlo simulation algorithm based on total least squares regression is given tomake a simulation solution for the Asian option pricing.Secondly: considering the volatility of the reality financial market and the uncertainty ofthe pricing model parameters, this paper introduces the fuzzy set theory, and assumes theuncertain parameters such as the underlying asset price, the volatility and the risk-free interestrate to be fuzzy numbers, making the Asian option price become a fuzzy number, and finallyestablishes the fuzzy pricing model for Asian option, and proposes the fuzzy pricing formulain the case of special fuzzy parameters. In practical applications, this paper established abi-directional mapping between a degree of membership and the fuzzy price: given an Asianoption invest price, its corresponding degree of membership can be obtained; given theinvestors’default membership, an investors’ reference price range can also be obtained. Basedon the bisection search algorithm proposed by Wu, this paper makes an improvement andproposes a interpolation search algorithm with faster computing speed for the calculation ofthe degree of membership. The fuzzy pricing model for Asian option established and theinterpolation search algorithm proposed in this paper can be well applied to the realityfinancial market, which can provide investors with investment decisions, and improve thepracticality of the model and the flexibility of investment.The empirical results show that the mutual combination of the two pricing methodsproposed in this paper can provide not only accurate Asian option price, but also a flexibleinvestment reference, and thus provide a strong strategy for the brokerage and investmentdecisions of investors in the market.