Research On Compound Option Pricing Of O-U Process Under Stochastic Interest Rate

With the rapid development of the financial derivatives market,the money market and the capital market are getting closer and closer,and gradually move toward a standardized and orderly development stage.As a new type of option,compound option has emerged in the market and has become a research hotspot of option pricing.A compound option is an option with an option as the underlying asset and an option on the option.In general,compound options are based on interest rates or foreign exchange,and the option contract itself is treated as a subject matter for option trading.When the volatility is high,investors spend money to avoid losses caused by rising prices.When the volatility is low,investors sell options to avoid losses due to price declines.In recent years,the theory and application of compound options have been widely concerned by scholars.At present,compound options have been widely used in practical issues such as asset valuation and portfolio analysis.Obviously,considering the compound option pricing problem under different circumstances is of great significance for financial market research.Based on the option pricing under the random interest rate and the O-U process theory of the index,the paper studies the European compound option pricing,which mainly solves two problems:First,on the basis of complete and no arbitrage in the financial market,the Hull-White stochastic interest rate model and the index O-U process are used to characterize the change law of interest rate and stock price respectively.Because asset price and interest rate have randomness and mean return characteristics,the adoption The method of calculating the unit of valuation is to first transform the measure.Then,using the Girsanov theorem,under the condition of satisfying the random interest rate of Hull-White,the compound option of the stock price following the index O-U process is analyzed,and the pricing formula is obtained,which expands the There is literature research.Second,taking full account of the self-similarity,thick tail and long-term correlation of asset prices and interest rates,in order to make the model closer to the actual market,the O-U process is added on the basis of the fractional jump-diffusion theory to expand the compound options.Assume that the interest rate of the compound option is subject to the Hull-White stochastic interest rate model,the asset price obeys the fractional jump-diffusion model with the O-U process,redefines the asset price by introducing white noise theory and Wick integral,and uses the actuarial method to obtain under the random interest rate of Hull-White,the compound option pricing formula of asset price obeying the fractional jump-diffusion O-U process further promotes the research of compound option pricing theory.Based on the above,this paper adds the O-U process to the compound option pricing under the condition of Hull-White's stochastic interest rate,fully considering the mean return of asset prices,and on this basis,the asset price is extended to the fractional jump-diffusion process.The relevant pricing formula is derived to make the asset price closer to the actual situation,and the compound option pricing theory is enriched and developed.