Hi,I'm wondering if someone can help clarify some confusion I have surrounding the use of physical and risk-neutralmeasures when computing the future exposure on an interest rate swap.Let's assume the correct approach is to simulate interest rate scenarios under the physical measure and thenprice instruments at future exposure dates using the risk-neutral measure. My confusion is the following: ifyou have simulated interest rates to some future date under the physical measure, doesn't this provide all thatyou need to price a swap on that date, since the value of the swap is just the sum of the discounted cash flows? How does the risk-neutral measure come into play?I would greatly appreciate anyone who could help set me straight on this, as I fear I am missing somethingat a basic level.Best,-P

I think you are mostly right. To be precise, if you have simulated the full yield curve to some future date under P, then you are indeed done; but if you have just simulated a set of state variables, e.g. in the simplest one-factor case, the short rate, you now need to recover the rest of the yield curve from them. This process would, in principle, require the calculation of some conditional "risk neutral" expectations, and if these were not available in closed form, you could find yourself mixing simulations under alternative measures.

"Risk neutral" expectations are used only when you calculate current value of options today or ones that start in the future in case when we buy hedged portfolio. It works at an infinitesimal period of time. If infinitesimal period is one day the value of the hedged portfolio should be adjusted. Such theoretical or practical adjustments should take place every day until next payment in say 6 months. a) We could not borrow value of the option at risk free rate b) the short selling of the underlying contract should be possible in the market otherwise application of the option pricing for irs is probably incorrect. We have implied forward rate concept for and stochastic model of the interest rate dynamics to calculate spot value of the IRS

QuoteOriginally posted by: pmb7if you have simulated interest rates to some future date under the physical measure, doesn't this provide all thatyou need to price a swap on that date, since the value of the swap is just the sum of the discounted cash flows? How does the risk-neutral measure come into play?yes, because a vanilla swap can be valued independently of a model. The difficulty of mixing the "outer" physical measure and the "inner" risk neutral measure only arises for instruments depending on some model dynamics like swaptions.

QuoteOriginally posted by: pcaspersQuoteOriginally posted by: pmb7if you have simulated interest rates to some future date under the physical measure, doesn't this provide all thatyou need to price a swap on that date, since the value of the swap is just the sum of the discounted cash flows? How does the risk-neutral measure come into play?yes, because a vanilla swap can be valued independently of a model. The difficulty of mixing the "outer" physical measure and the "inner" risk neutral measure only arises for instruments depending on some model dynamics like swaptions.and there is no evidence why we call solution of the BSE price if we use it outside of hedged portfolio

QuoteOriginally posted by: list1QuoteOriginally posted by: pcaspersQuoteOriginally posted by: pmb7if you have simulated interest rates to some future date under the physical measure, doesn't this provide all thatyou need to price a swap on that date, since the value of the swap is just the sum of the discounted cash flows? How does the risk-neutral measure come into play?yes, because a vanilla swap can be valued independently of a model. The difficulty of mixing the "outer" physical measure and the "inner" risk neutral measure only arises for instruments depending on some model dynamics like swaptions.and there is no evidence why we call solution of the BSE price if we use it outside of hedged portfolioI think that is enough for now.

It should be clear that BS option price itself is the solution of BSE. It is characterised as a smooth non random function of ( t , S ) which promises to investor instantaneous rate of return equal to risk free plus return of delta shares of underlying stocks. Delta is known and instantaneous stock return is "white noise" type random process. It follows from formula of the rate of return of the hedged portfolio. When we do talk about rate of return of the hedged portfolio it looking good but we could not say similar words regarding components of the hedged portfolio. Sum of components is riskless while each of components is risky. Situation is pretty similar to the standard calculus examples when a sequence B_n - D_n converges to a finite limit while each of the B_n , D_n does not.

QuoteOriginally posted by: outrunlist1 , please stop hijacking threads with BSI did not want to upset somebody about BS. It seems to me that anything what I did say about BS pricing is directly follow from its definition with the help of hedged portfolio. Some facts that I highlighted such as for example that BSE solution has risky rate of return is probably obvious but never mentioned in handbooks but it looks important for investors and therefore for market too. If I am wrong one can correct me. I think that hijacking is too strong words here. I do think that if you represent your arguments against my point on BS pricing it will be a good proof that I am wrong. We are talking about well known subjects and Willmott is probably the best place in the world for open discussion. There quite a large number well known professors here that knows Finance better than me.

QuoteOriginally posted by: list1QuoteOriginally posted by: outrunlist1 , please stop hijacking threads with BSI did not want to upset somebody about BS. It seems to me that anything what I did say about BS pricing is directly follow from its definition with the help of hedged portfolio. Some facts that I highlighted such as for example that BSE solution has risky rate of return is probably obvious but never mentioned in handbooks but it looks important for investors and therefore for market too. If I am wrong one can correct me. I think that hijacking is too strong words here. I do think that if you represent your arguments against my point on BS pricing it will be a good proof that I am wrong. We are talking about well known subjects and Willmott is probably the best place in the world for open discussion. There quite a large number well known professors here that knows Finance better than me.Two separate points. First, the original poster made a perfectly reasonable inquiry with some practical real world implications. He made it in the right forum, and he received a couple of what I hope/think to be useful replies. Then you come wading in with your agenda, which has nothing to do with the topic at hand. Second, we have tried to correct you on more occasions than I can count, and you appear to be incorrigible. Finally, as a matter of interpretation, I don't think outrun was referring to Black-Scholes...

one can read in title of the original message words risk neutral measure which directly relates to BS concept of pricing. In your response one can see two different approaches on IRS pricing. One based on BS concept and other on stochastic interest model. Indeed fixed rate payer cash flow represents series of long call options and short put options and the BS pricing suggests to use risk neutral underlying to calculate PV of the cash flow. My problem is that whether we can use BS option pricing outside of the BS hedged portfolio. For me "no free lunch" popular slogan is related to BS portfolio but not to call option itself and this slogan is inapplicable to call option. Though in time when this slogan was popular it seemed to me that it was directed to BS call option price itself. I do not sure that asking such questions is something that one can identify as hijacking threads

QuoteOriginally posted by: outrunQuoteOriginally posted by: bearishQuoteOriginally posted by: list1QuoteOriginally posted by: outrunlist1 , please stop hijacking threads with BSI did not want to upset somebody about BS. It seems to me that anything what I did say about BS pricing is directly follow from its definition with the help of hedged portfolio. Some facts that I highlighted such as for example that BSE solution has risky rate of return is probably obvious but never mentioned in handbooks but it looks important for investors and therefore for market too. If I am wrong one can correct me. I think that hijacking is too strong words here. I do think that if you represent your arguments against my point on BS pricing it will be a good proof that I am wrong. We are talking about well known subjects and Willmott is probably the best place in the world for open discussion. There quite a large number well known professors here that knows Finance better than me.Two separate points. First, the original poster made a perfectly reasonable inquiry with some practical real world implications. He made it in the right forum, and he received a couple of what I hope/think to be useful replies. Then you come wading in with your agenda, which has nothing to do with the topic at hand. Second, we have tried to correct you on more occasions than I can count, and you appear to be incorrigible. Finally, as a matter of interpretation, I don't think outrun was referring to Black-Scholes...Yes, those are my points too, well said and clear.And your new post is again wrong "...relates to BS concept of pricing" is your personal obsession and *not* of any importance in this discussion. Every time we talk about food you can try to bend the discussion to bananas, but it's irritating, dumb, selfish and spammy.

outrun, bearishyou are talking about my wrong points but do not specify it. Show me where I am wrong or that it is known facts referring on a source. I say 1. BS derivation of the BSE is based on hedged portfolio. Therefore we can and should use BSE solution as an option price when we construct a hedged portfolio2. Buying option itself for BSE solution as a price is*) risky. There is no evidence why BS price can be called option price outside of hedged portfolio pricing setting. Primary risk characteristics say average profit and average loss of the naked option are ignoring or misunderstanding.What is wrong here?