On the implied market price of risk under the stochastic numéraire

Abstract

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. An equivalent martingale measure is not unique for this market, and there are non-replicable claims. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from bond prices constructed as a risk-free investment with deterministic payoff at the terminal time. This leads to possibility to infer a implied market price of risk process from observed historical bond prices.

A gap between rational annuitization price for producer and price for customer

“…This would follow a classical approach where the inference of the volatility of the stock prices is reduced to calculation of the implied volatility from the inverted Black-Scholes pricing formula applied to stock option prices. Examples of extensions of this approach can be found in Dokuchaev (2018) and Hin and Dokuchaev (2016a,b). So far, the implied market parameters for the annuities market have not been considered in the literature.…”