Hi Adrien,
>Hi,
>can someone explain to me why it could be useful to
>use future price instead of cash price in
>Black-Scholes option pricing formula?
>Thanks
>Adrien
In the BS option pricing formula for bonds, you use the forward price of the
bond. Why? This is to comply with the pull-to-par effect, which simlpy
states that the price at the maturity of a bond is equal to the principal
plus the coupon, i.e. a non-random value. Thus, the price vol has to be zero
at that point. If you use forward prices and also forward vols, you can
circumvent the problem of the constant vol in the standard BS. The extreme
example is a European option on a bond, where the expiry date of the option
is equal to the maturity of the bond. In that case, we know with certainty
what the price of the bond is at expiry of the option. Its forward vol is
also correctly equal to zero in the adjusted BS. In the standard BS this vol
would be non-zero.
Gilbert
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