Academic journal article The International Journal of Business and Finance Research

Pricing of Payment Deferred Vulnerable Options and Its Application to Vulnerable Range Accrual Notes

Academic journal article The International Journal of Business and Finance Research

Pricing of Payment Deferred Vulnerable Options and Its Application to Vulnerable Range Accrual Notes

Article excerpt

ABSTRACT

This paper derives a pricing model for payment deferred vulnerable options and applies the results to the pricing of vulnerable range accrual notes. The valuation model for vulnerable options takes into account the possibility of the option writer defaulting. However, when the payment date is set later than the option maturity date, the valuation model will be incomplete if the default risk between the option maturity and payment dates is not explicitly incorporated. We extend the current available models and our results show that the default risk of the option writer will further reduce the option value if the payment date is after the maturity date. The analysis of vulnerable range accrual note, which contains multiple payment deferred vulnerable options, is also performed. Due to the product design, the pricing model for vulnerable range accrual notes shows that the relationship between volatility and note value is not monotonic but depends on whether the underlying price is within, outside, or on the range boundary.

JEL: G12; G13

KEYWORDS: Reduced form model, vulnerable options, vulnerable range accrual notes

(ProQuest: ... denotes formulae omitted.)

INTRODUCTION

This paper derives a pricing model for payment deferred vulnerable options and applies the results to the pricing of vulnerable range accrual notes. The valuation model for vulnerable options takes into account the fact that the option writer may default. However, when the payment date is set later than the option maturity date, a common arrangement in the OTC structured products market, the valuation model will be incomplete if the default risk between the option maturity and payment dates is not explicitly incorporated. We extend the current available models, which usually assume that the option maturity and payment dates are identical. Our results show that the default risk of the option writer will further reduce the option value if the payment date is after the maturity date.

One practical application of the payment deferred vulnerable option valuation model is in the valuation of vulnerable range accrual notes. Range accrual notes are structured products. Its payoff is defined as the interest payment computed as the proportion of the number of days that the reference underlying asset price lies within a specified range times the interest rate specified at the initiation of the note. The specified interest rate is usually set much higher than the interest rate currently available on the market. Therefore, it gives the note holders a chance to get higher earnings. For this reason, the range accrual note is attractive to investors, especially in a low interest rate environment. The analysis of vulnerable range accrual note, which contains multiple payment deferred vulnerable options, is also performed.

The paper is organized as follows. Section 2 provides a pricing model for payment deferred options. Since range accrual notes can be regarded as combinations of range options, which are combinations of digital options, Section 3 discusses the valuation of digital options and range options. Section 4 then applies the results in Sections 2 and 3 to the pricing of vulnerable range accrual notes. Finally, Section 5 presents our conclusions.

LITERATURE REVIEW

Black and Sholes (1973) value options by constructing a no-arbitrage portfolio and employ the partial differential equation (PDE) technique to derive the closed-form solution for European options. The martingale pricing method (Harrison and Kreps, 1979; Harrison and Pliska, 1981) is efficient in reducing the complexity of pricing processes, and it is now widely used in option valuation. Cox, Ross, and Rubinstein (1979) propose the binomial option pricing model that can handle various types of options, especially American options. For more complex options such as path-dependent options, it is more suitable to apply the Monte Carlo simulation method (Boyle, 1977). …

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