Real-world expected cash flow profile for derivatives

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approximated
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Joined: Wed Jul 14, 2010 11:42 pm

Real-world expected cash flow profile for derivatives

Postby approximated » Sat Oct 20, 2012 6:16 pm

Dear Professor,

I'm trying to understand how to express the current expected cash flow profile related to a set of derivatives. The point of view, here, is the one of an analyst interested in the liquidity profile of these contracts.

Suppose a portfolio containing an IRS floating-receiver (or a long FRN, if you consider this as an IR derivative) and a Cap.

To report the cash flow profile of the receiving leg of the swap the widely used approach seem to be the use of the current forward curve to obtain the future cash flows related to the floating leg of the contract. Starting from the current spot curve, the relevant forward rate implied in this curve are the unbiased estimation of the future floating rate (suppore 6 months Libor) to receive on each reset date.
The forward rate implied in the current spot curve is an unbiased estimation of the future Libor rate in a T-forward risk neutral world. If one would use the corresponding future rate this will be an unbiased estimation of the future level of the 6 months Libor in a risk neutral world.
In both cases, the cash flows obtained by using forward/future rates are not real world expectetion. If I want to see the liquidity cash flow profile of a contract I'm interested in the real worl expectation of the risk factor in order to find the future expected cash flows.

For pricing purposes the cash flows obtained using forward or future are then discounted (T-ZCB in case of forward, money market account in case of future) so there are no problem.

But what if I want to find the real-world expected cash flow profile? Why the banking industry continues to use the implied forward rates as expectation of the future level of the risk factor (and cash flow)?

In addition, consider a Cap, composed by two Caplet. The payoff is max(L - Strike, 0) where L is the future Libor rate to be observed.
How should the cash flows related to this position be reported to asses the expected liquidity cash flow profile?
The problem here is similar to that of the IRS. One need a real-world expectation for L and implied in the current spot curve there's just a T-forward expectation of this variable.
In this case there's another issue. Being an option, there's the problem of the asimmetry... Why should I report a given cash flow at the maturity of each Caplet (the cash flow being a function of the real-world expectation of the Libor rate) if this cash flow will occur only in the expected rate L will be higher than the strike? I should weight this expected cash flow by the probability of the Caplet to be exercised. But how to find such real-world probability?
The delta of the option is a proxy of this probability but only in a risk neutral environment.
The problem of the switch from a risk neutral world to a real world here seem to be evident.

How should one fix these problems? What is really done in the banking industry?

Thanks a lot!

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