| As a tool hedging volatility risk,volatility derivatives have played an important role in asset portfolio and risk aversion,thus attracting more and more investors.As two of the more popular volatility derivatives,the study of variance swaps and volatility swaps has also attracted more and more attention from scholars.Both variance swaps and volatility swaps are essentially forward contracts,and the payoff depends on the realized variance or volatility of the underlying asset price during the term of the contract.Considering that the major emergencies in the financial market can lead to sharp fluctuations in asset prices,this paper adds jump diffusion to the model of volatility swaps to describe the impact of this phenomenon on the price of the underlying asset.At the same time,in order to fit the operation of the actual financial market,this paper considers the pricing problem in discrete cases.Through the independence of Brownian motion and compound Poisson process,we can decompose the Heston model with jump diffusion into two parts and calculate the realized volatility separately.On the specific form of jump diffusion,we introduce a normal distributed Merton model and Kou model with double exponential distribution,and finally give an upper bound on the fair strike price of volatility swaps and present a closed-form exact solution for the price of variance swaps in both circumstances. |
