Application of a variable default boundary to the pricing of vulnerable European options: the use of a three dimensional binomial tree

This paper investigates the significance of using a variable default boundary when pricing European Black-Scholes options that are subjected to credit risks. We apply numerical method and combine Klein [1], and Johnson and Stulz [2] to link the payout ratio proportionally to the assets of the option writer. We also link the payout ratio to the value of the assets of the writer. Numerical examples compare our results with Klein [1], and Johnson and Stulz [2] based on alternative assumptions, and illustrate when the application of variable default boundary becomes important.