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Enron Mail |
John,
I think the crucial distinction is between recognition of risks and elimination of risks through hedges (as correctly pointed out in other messages). Being aware of risk does not mean that one does not want to be compensated for it. Now a few more detailed comments. 1. I think that illiquidity discount represents double counting when combined with a project finance discount rate. Illiquidity discount, in my view, should be applied to financial options that trade in a market without sufficient depth. One should apply a haircut if liquidating a position takes a long time. The approach used in valuation of the Turkish transaction is the same as approach used in valuation of investments in physical assets, which are by definition illiquid. This illiquidity is recognized through other aspects of valuation technology used in RAROC. If we apply an illiquidity correction in this case, we should be consistent and use this approach across the board for all project finance type cases (not that I recommend this course of action). 2. Valuation of an unheadgable options. Let's look at it from the position of a seller of the option. He cannot hedge a short call or put and Black-Scholes valuation becomes the floor for the valuation: the seller has to be compensated for taking a price risk (as opposed to taking a vol risk when he hedges). The issue of the compensation he will require becomes fuzzy. The option really becomes an insurance type product and pricing depends on two factors: 1. risk preference 2. existing portfolio positions Risk preference. Insurance companies typically require a payment that consists of two parts: expected loss + unexpected loss. The latter is typically defined as 1 to 2 standard deviations. The number of standard deviations depends on risk appetite and the ability to absorb the loss. I admit that it is a bit fuzzy, but this is the way the world works. We looked into insurance pricing at the request of Jere Overdyke. You can talk to Vasant Shanbhogue to find out more about it. Existing portfolio positions. An additional contract may increase or decrease the risk of the overall portfolio. I would expect the deal to provide some risk diversification, but it does not look to me as a deal that reduces risk (given all our positions in this region). What are the practical implications? Pricing depends on risk appetite (the utility function of a decision maker in technical jargon) and becomes to some degree arbitrary. If we are short an option embedded in a deal and the option cannot be hedged, we should subtract from the value of the contract the value of the option (that is greater than the Black - Scholes value). If we don't price this option explicitly, the valuation of a contract will be based on a discount rate with a risk premium. In the case of an option buyer, the situation is reversed. If he cannot hedge, he should recognize the risk of losing the value of his investment and apply a discount to the value of the option. How big is the discount? See the comments above. In the special case, where hedging is possible and the Black-Scholes-Merton paradigm applies, both values will become equal (ignoring transaction costs). The values of an option form the point of view of a seller and a buyer will converge. 3. What happens in case we use simulation technology? We can discount at the risk free rate along each scenario (each scenario will recognize the downside and/or upside at different points in time in different states of the world). If we run a sufficient number of scenarios, we shall get a distribution of NPV as of today. Knowing this distribution means that we can estimate risk, but in most cases we are still holding it. The expected value should be, therefore, adjusted for risk. This is equivalent to using a discount rate with a risk premium. I hope this helps. Please, call me with additional questions. Sorry for a delay in responding to this question. I ran my response by Stinson and Vasant, to make sure we all agree. It's a very complicated technical problem and the financial theory does not have good answers. Vince
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