This article develops a discrete-time, risk-neutral valuation relation (RNVR) for the pricing of contingent claims when preferences in the economy are characterized by decreasing absolute risk aversion and the marginal distribution of the underlying is an inverse coshnormal. The RNVR is applied to obtain closed-form expressions for calls and puts written on nondividend-paying stocks, futures contracts, foreign currencies, and dividend-paying stocks. Such pricing equations contain two parameters, the threshold and rescale parameters, not contained in the Black–Scholes valuation equation. Inverse-coshnormal option values make the approach look interesting. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1091–1117, 2001