Near Exact Calculation of American Options

A new practical approach for the analysis of American (bond) options is developed which is a combination of the closed form solutions and binomial lattice models. The model is calibrated to the observed term structure of rates and traded volatilities and is arbitrage free. The convergence is very fast, but numerically intensive. By extrapolation the near exact premium of an American (bond) option can be calculated

Adjustment to Risk Free Rate/ Violation of Put-Call Parity

The present value of a forward contract for any asset that does not pay a dividend is calculated by discounting its forward price by the risk-free rate. We show that the discount function for assets that have a non-zero correlation with interest rates, has to be adjusted to account for the correlation between the asset and interest rates. Put-Call parity is also violated and needs to be adjusted as well for such assets. It is shown that the risk-free rate is asset dependent. The adjustment to the price is small for short dated forwards, but increases quadratically with time to maturity