w********r
发帖数: 9 | 1 The BS equation:
df/dt + \mu*S df/ds +1/2 \delta^2*S^2 d^2f/ds^2 = \mu f
Take f = 1/S
then -\mu/S + \delta^2/S = \mu/S
so (2*\mu - \delta^2) /S = 0
it does not make sense to me, but I donot know why. Somebody please help,
thanks! |
f******y
发帖数: 2971 | 2 This is a logical error. What you know is f(T) = 1 / S(T). If you know f(t)
= 1/S(t), why do you bother BS equation? It is actually wrong to use BS in
that case. |
w********r
发帖数: 9 | 3 So the BS was derived under the arbitrage free environment. If we define an
arbitrary option, it may produce arbitrage or other contradiction on the
assumptions. I guess |
p*****k
发帖数: 318 | 4 wondererer, are you saying the final payoff of some option is
1/S(T) and you need to price it?
it's a boundary condition for your PDE instead of the solution
(but probably taking discounted expectation under risk-neutral
measure would be easier) |
w********r
发帖数: 9 | 5 Yes. It only makes sense when 1/S(T) is the boundary not the solution. I did
not figure that out as i posted this article. |
