Pricing Credit Default Swaps With Counterparty Risk Under Dynamic Games

In the framework of the reduction model,this paper calculates the fair price of credit default swaps containing the credit risk of bilateral counterparties,and uses the complete information game and incomplete information game to calculate the contract price in the over-the-counter market based on the fair priceFirst calculate the price of the fair contract.The Markov Copula method is used to model the default correlation of credit default swaps with bilateral counterparty risk,and then calculate the cash flows of the contract buyer and contract seller.From the expected cash flow at the initial moment,the fair price of a credit default swap containing the credit risk of bilateral counterparties is obtainedSecondly,under the complete information game,calculate the contract price of OTC.It is assumed that the utility functions of the buyer and seller regarding the contract are both power utility functions.The seller assumes that the buyer's reservation price for the contract is uniformly distributed over[0,1],and the buyer assumes that the seller's reservation price for the contract is also uniformly distributed over[0,1].Buyers and sellers each bid with the goal of maximizing their expected utility.Based on the complete information game and the bidder's bids,the conclusion of the bargaining game under infinite time is used to calculate the contract price of the off-exchange market transaction under the complete information game.Finally,the contract price of over-the-counter transactions is calculated under an incomplete information game.It is assumed that the buyer's reservation price for the contract is non-public information,and only the buyer knows it.The seller and the buyer play a three-round game.In each round,the seller bids,and the buyer chooses to accept or reject it.The seller speculates that the buyer's reservation price for the contract is evenly distributed and bids based on maximizing his expected utility.The seller continuously adjusts the upper bound of the buyer's reserve price estimation based on the buyer's response after each round of bidding,and finally calculates the contract price of the off-exchange market transaction under incomplete information games.