3 votes
Accepted

Hedging gamma, theta or other risks

In the Black-Scholes model Gamma and theta do not need to be hedged because the BS PDE says that they balance each other (I'll take $r = 0$): $$ \frac{\partial f}{\partial t} + \frac12 \sigma^2 S^2\...
Frido's user avatar
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2 votes

Why A Derivative With Intrinsic Arbitrage Cannot Be Valued & Hedged With Assets In Risk Neutral?

Valuing something to the writer vs valuing it to the buyer makes no difference. We just value the instrument. In this case the buyer surely would prevent the writer from collecting the fee, by ...
dm63's user avatar
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1 vote
Accepted

In Black-1976, why is the differential equation missing a term relative to B-S?

$w_1$ is also known as $\Delta$. And $x \Delta$ is the value of the hedging position, so $r x \Delta$ is the instantaneous cost of financing the hedging position. Since as you say futures have no ...
nbbo2's user avatar
  • 11.2k
1 vote

Trying to follow course notes deriving Black-scholes PDE, but I can't fill in the gaps

Sometimes I wonder how did I get my math degree. "Just take the partials and substitute to the original to get the original PDE". Quite literally. Recall we have $F(t, s) = \exp(rt)H(t, s)$, ...
AyamGorengPedes's user avatar
1 vote

Trying to follow course notes deriving Black-scholes PDE, but I can't fill in the gaps

First, I suggest looking at the first derivation in this this link from Fabrice Rouah. While there are a few derivations of the BS PDE (and several in that file), this is one a lot of people will be ...
Rylan's user avatar
  • 410

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