Risk-neutral Approach Research Articles

A risk-neutral approach to option pricing with jumps and diffusion

A risk-neutral approach to option pricing with jumps and diffusion

Risk-neutral Valuation: A Gentle Introduction (2)

This teaching note is a continuation of the previous teaching note on risk-neutral valuation. In Section One, we estimate the value of levered equity in a levered company in an M & M world with risk-free debt and without taxes. The structure of the presentation will facilitate the subsequent analysis with taxes. We find the value of the levered firm in two ways. First, we use the replicating portfolio method. Second, we use the risk-neutral approach, which is equivalent to the replicating portfolio method. In Section Two, we analyze risky debt in a world without taxes. In Section Three, we introduce taxes. However, we continue to assume risk-free debt. The risk of the tax shield is indeterminate. In Section Four, we analyze risky debt in the presence of taxes and derive the relevant expressions for the returns to the equity and debt holders.

Risk-neutral Valuation: A Gentle Introduction (1)

Risk-neutral valuation is simple, elegant and central in option pricing theory. However, in teaching risk-neutral valuation, it is not easy to explain the concept of 'risk-neutral' probabilities. Beginners who are new to risk-neutral valuation always have lingering doubts about the validity of the probabilities. What do the probabilities really mean? Are they real or fictional? Where do they come from? What is the relationship between the risk-neutral probabilities and the actual probabilities? Does it mean that all investors are risk-neutral? When is it appropriate to use the risk-free rate as the discount rate? From a pedagogical point of view, in the beginning it is best to avoid the use of probabilities because probabilities can be a barrier to understanding. Instead, it is far preferable to introduce the idea of state prices and then show that the approach with risk-neutral probabilities is equivalent to the use of state prices. In this teaching note, we use simple one-period examples to explain the intuitive ideas behind risk-neutral valuation. It is a gentle introduction to risk-neutral valuation, with a minimum requirement of mathematics and prior knowledge. We will provide the motivation and the rationale for calculating state prices and we will show that the risk-neutral approach is simply another way of looking at the issue of state prices.

Cost-effectiveness analysis with risk aversion.

This paper discusses why, in a medical context, the standard assumption of a risk-neutral social planner is inappropriate and develops a framework for conducting cost-effectiveness (CE) analysis when social planners are risk-averse. This framework demonstrates that if new medical interventions are variance increasing (decreasing), the risk-neutral approach will approve (reject) projects that should be rejected (accepted). This methodology is applied to two medical interventions that have been previously evaluated and considered cost-effective in the published literature. Since both conclusions assumed risk neutrality we determine the level of societal risk-aversion that would be necessary to reject these new interventions and compare these levels to previous estimates of risk-aversion in the economics literature. We find that for reasonable values of the risk-aversion parameter, only one of the two interventions should be approved. It is our recommendation that the cut-off risk aversion parameter (the level of risk-aversion above which a project would be rejected) should become a standard reported figure in future CE studies.