Abstract
Abstract The pricing and hedging of financial derivatives have become one of the hot research issues in mathematical finance today. In the case of non-risk neutrality, this article uses the martingale method and probability measurement method to study the pricing method and hedging strategy of financial derivatives. This paper also further studies the hedging strategy of financial derivatives in the incomplete market based on the BSM model and converts the solution of this problem into solving a vector on the Hilbert space to its closure. The problem of space projection is to use projection theory to decompose financial derivatives under a given martingale measure. In the imperfect market, the vertical projection theory is used to obtain the approximate pricing method and hedging strategy of financial derivatives in which the underlying asset follows the martingale process; the projection theory is further expanded, and the pricing problem of financial derivatives under the mixed-asset portfolio is obtained. Approximate pricing of financial derivatives; in the discrete state, the hedging investment strategy of financial derivatives H in the imperfect market is found through the method of variance approximation.
Highlights
Financial derivatives are derived from basic financial assets and are a very important part of global financial innovation in the 1970s and 1980s
Financial derivatives can be divided into four types of contracts: forwards, futures, options and swaps according to their own product forms [1,2]
If divided according to the relationship between the price of financial derivatives and the price of its underlying assets, financial derivatives can be divided into two categories: linear derivatives and non-linear derivatives: linear derivatives include forward contracts and futures contracts With swap contracts, there is a linear relationship between the price of such derivatives and the price of the underlying asset; nonlinear derivatives include options, structured derivative securities, and exotic derivative securities, and their prices are very close to the price of the underlying asset [3, 4]
Summary
Financial derivatives are derived from basic financial assets and are a very important part of global financial innovation in the 1970s and 1980s. Financial derivatives can be divided into four types of contracts: forwards, futures, options and swaps according to their own product forms [1,2]. If divided according to the relationship between the price of financial derivatives and the price of its underlying assets, financial derivatives can be divided into two categories: linear derivatives and non-linear derivatives: linear derivatives include forward contracts and futures contracts With swap contracts, there is a linear relationship between the price of such derivatives and the price of the underlying asset; nonlinear derivatives include options, structured derivative securities, and exotic derivative securities, and their prices are very close to the price of the underlying asset [3, 4]. This article mainly studies the pricing and hedging of nonlinear derivatives, which mainly refers to the pricing and hedging of options
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