Abstract
In over-the-counter markets, many options on defaultable instruments are influenced by default risks emanating from the possibility that the option writer may not fulfill its contractual obligations. In this paper, we investigate the valuation of fixed-strike lookback options based on the issuer’s credit risk. Using double Mellin transforms and the method of images, we have a closed-form solution to fixed-strike lookback options with a default risk. Furthermore, we analyze the values of the vulnerable fixed-strike lookback options with respect to the model parameters and also show that the Monte Carlo simulations and the Implicit Finite Difference Method converge to the closed-form solutions and this verifies the correctness of our formulas.
Highlights
Since the global financial and Eurozone crises in 2007–2008, there have been quickly increasing concerns regarding financial derivatives, which are more likely to be exposed to credit default risk in over-the-counter (OTC) markets
To derive the pricing formula for vulnerable fixed-strike lookback options (VFSLOs), we exploit the Mellin transform approach, and the method of images presented in Eltayeb and Kilicman [13] and Buchen [14], respectively
We examined the closed-form formula of a fixed-strike lookback option (FSLO) with default risk of
Summary
Since the global financial and Eurozone crises in 2007–2008, there have been quickly increasing concerns regarding financial derivatives, which are more likely to be exposed to credit default risk in over-the-counter (OTC) markets. To derive the pricing formula for vulnerable fixed-strike lookback options (VFSLOs), we exploit the Mellin transform approach, and the method of images presented in Eltayeb and Kilicman [13] and Buchen [14], respectively. Jeon et al [21] derived the vulnerable path-dependent option prices using a double Mellin transform and the method of images.
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