Bond Options and Swaptions Pricing : A Computational Investigation of Volatility Inference

Derivative pricing is especially challenging in novel and illiquid markets, where pricing relies greatly on assumptions and models, rather than on known flow of market prices. In the novel market of shekel bond options, the estimate of implied volatility for different strikes could be based on the information about other -- sometimes more liquid -- financial instruments in the market. Here we show relevance, but not equivalence, of the information from the market of swaps, (volatility of swap rates), to the market of bonds, (volatility of bond prices). In particular, we show why the proxy to bond's yield to maturity from the swap market should be based on the swap rate maturing simultaneously with the bond. Numerical simulations and analysis of historical data are applied to examine the approximation and assumptions which, in the presence of swaption market, can be applicable for inferring information about bond price volatility smile. Hypothetically, the procedure is invertible -- inferring information about swap rate volatility smile, based on the data from the bond options market. Our analysis is implemented for the Israeli market, while the rationale is relevant for similar instruments elsewhere