Unified Treatment of Average-Rate Contingent Claims with Applications PDF Download

Author: Dilip B. Madan
Publisher:
ISBN:
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Languages : en
Pages : 40

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Book Description
This article studies the valuation of average-rate contingent claims (both arithmetic and geometric), whose importance in corporate risk management is increasing rapidly. Arbitrage--free characterizations are provided for such option--like Asian claims. When the spot price is governed by a one-dimensional Markov diffusion, we examine analytically the response of the average-rate option claim to a change in (i) the underlying spot price; (ii) the average-to-date price dependence; (iii) the riskiness of the asset; (iv) the strike price; (v) the interest rate; and (vi) the dividend/convenience yield. Our analysis yields the distinctive outcome that the upper bound on the average-rate call option delta can depart significantly from the classic unity. Depending on the structure of the risk-neutral density, a lower average-rate option premium (relative to the traditional option) is also internally consistent. Marking a sharp contrast from convention, the average-rate call can be decreasing in the interest rate. In extending the above general characterizations to higher dimensional contexts, we offer tractable valuation formulas for (1) options on the average interest rate with stochastic volatility; (2) catastrophe insurance option contract; and (3) options on the average commodity futures price [with stochastic convenience yield and stochastic interest rate]. Each valuation formula is rich in its economic content and yet amenable to empirical implementation. This paper has developed a cohesive framework for the valuation of average-rate contingent securities.