A Note on the Call - Put Parity and a Call - Put Duality

A Note on the Call-Put Parity and a Call-Put Duality

Along with the well-known “call-put parity” relation, that makes it possible to express the rational price of a put option in terms of the rational price of a call option, we introduce a “call-put duality” relation. This new concept offers a simple explanation of the relationship between the rational price of a put option and a call option, not only for options of the European type, but also fo...

A Call-Put Duality for Perpetual American Options

It is well known [5], [1] that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper investigates such a Call Put duality for perpetual American options. It...

American Put Call Symmetry

We derive a simple relationship between the values and exercise boundaries of American puts and calls. The relationship holds for options with the same \moneyness", although the absolute level of the strike price and underlying may di er. The result holds in both the Black Scholes model and in a more general di usion setting. We thank Neil Chriss, the editor, and two anonymous referees for thei...

Put-call Symmetry: Extensions and Applications

Classic put-call symmetry relates the prices of puts and calls at strikes on opposite sides of the forward price. We extend put-call symmetry in several directions. Relaxing the assumptions, we generalize to unified local/stochastic volatility models and time-changed Lévy processes, under a symmetry condition. Further relaxing the assumptions, we generalize to various asymmetric dynamics. Exten...

Multivariate Extension of Put-Call Symmetry