Risk-Neutral Pricing Method for Credit Risk and Empirical Evidences from China
The basic theories of pricing interest rate derivatives include winner process, Ito process, martingale, differential equation as well as risk-neutral pricing, no-arbitrage principle and assets pricing theorem etc.
From the broad definition of option, this paper derives the concept of real option. Further, based on theories of net present value, decision tree, and real options, the risk-neutral pricing theory is introduced.
In detail we have made main conclusions as follows:(1)Under the hypothesis of exponential O-U model and constant interest rate ,using risk-neutral pricing principle, we obtain the pricing formulas of lookback option in two cases of fixed strike price and floating strike price,and the put-call parity relation is deduced;
This paper is based on the suppose of Black-Scholes. By using the risk neutral pricing theory of option and analysising the martingale property of the asset value process, we construct the model of the value of barrier options.
Thirdly, Pricing EIA Under the Credit Risk(First Part). In this chapter, we get the pricing and reserve structure under the point to point index method, assuming that rate of recovery is 1.We use the risk neutral pricing, risk minimizing strategy, percentile principle etc.
Through the stochastic discount factor model, it is easy to understand some classical problems of modern finance, such as arbitrage pricing theory and risk neutral pricing, etc. Asset pricing models are unified under the stochastic discount factor frame.
Risk-neutral valuation is discussed and a simple jump-diffusion model is chosen to illustrate the results.
Valuing executive stock options is a challenging problem, because the standard risk-neutral valuation of those options is not appropriate; the executive is not allowed to trade the stock of the firm, so is not operating in a complete market.
As this paper shows, an executive holding many American-style call options on his firm's stock will optimally exercise the options bit by bit, whereas a risk-neutral valuation of the options would assume that all are exercised at the same time.
Dual ones allow us to extend the risk-neutral valuation methodology for imperfect and noarbitrage free markets and provide new interpretations for the measures in terms of "frictions effect" or "committed errors" in the valuation process.
The risk-neutral valuation formula for path-dependent options contingent upon multiple underlying assets admits an elegant representation in terms of path integrals (Feynman-Kac formula).