Pricing of Vulnerable Timer Options

First introduced by Societe Generale Corporate and Investment Banking in 2007, timer options are financial instruments whose payoffs rely on a random date of the exercise related to the realized variance of the underlying asset. This is contrary to vanilla options exercised at a fixed expiration date. However, option holders are vulnerable to credit risks arising from the uncertainty that counterparties may not implement their contractual obligation, particularly in the over-the-counter market. Hence, in this article, motivated by the credit risk model proposed by Johnson and Stulz (JFinac 42:281-300, 1987), we deal with the pricing of the timer option considering the counterparty default risk by utilizing the technique of asymptotic analysis. Moreover, we investigate the pricing accuracy of our analytic formulas, comparing them with the solutions from the Monte Carlo method, and examine the impact of stochastic volatility on the credit risk or the variance budget on the option value based on our pricing formula for vulnerable timer options.