The valuation of multivariate contingent claims under transformed trinomial approaches

This study develops a transformed-trinomial approach for the valuation of contingent claims written on multiple underlying assets. Our model is characterized by an extension of the Camara and Chung (J Futur Mark 26: 759–787, 2006) transformed-binomial model for pricing options with one underlying asset, and a discrete-time version of the Schroder (J Finance 59(5): 2375–2401, 2004) model. However, unlike the Schroder model, our model can facilitate straightforward valuation of American-style multivariate contingent claims. The major advantage of our transformed-trinomial approach is that it can easily tackle the volatility skew observed within the markets. We go on to use numerical examples to demonstrate the way in which our transformed-trinomial approach can be utilized for the valuation of multivariate contingent claims, such as binary options.