Arbitrage-Free Pricing of XVA for American Options in Discrete Time Public
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Total valuation adjustment (XVA) is a new technique which takes multiple material financial factors into consideration when pricing derivatives. This paper explores how funding costs and counterparty credit risk affect pricing the American option based on no-arbitrage analysis. We review previous studies of European option pricing with different funding costs. The conclusions help to compute the no- arbitrage price of the American option in the model with different borrowing and lending rates. Another model with counterparty credit risk is set up, and this pricing approach is referred to as credit valuation adjustment (CVA). A defaultable bond issued by the counterparty is used to hedge the loss from the option's default. We incorporate these two models to assess the XVA of an American option. The collateral, which protects the option investors from default, is considered in our benchmark model. To illustrate our results, numerical experiments are designed to demonstrate the relationship between XVA and parameters, which include the funding rates, bond's rate of return, and number of periods.
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