So we all know that we need "detla" units of the underlying to hedge a position in a call, and under black scholes, delta = dC/dS = N(d1), because C = SN(d1) - e^(-rt)K(Nd2), but then this assumes that the underlying actually follows geometric brownian motion. What makes anyone believe that actual price of the call and the underlying in the markets (which you see on your bloomberg screen), are related by black scholes? are any other methods used to "delta hedge", besides black scholes?
Trending Content - Sales and Trading Forum
Career Resources
black scholes is just an approximation, as it assumes a flat volatility surface. many banks have models that incorporate market data into an actual (non-constant) vol surface as a snapshot in time, which is then used as an input for models that determine your greek exposure. an even then, these models are just the best approximation available. the idea is that using this to delta-hedge gets you "close enough" and flattens your risk as much as possible. no model is perfect.
.....
From a commodities and FX perspective:
In real life, an options book on an active desk is pretty much never perfectly delta hedged, even when the team wants to be delta neutral. In the time it takes to make the trades that hedge what you think your delta is, and then have the risk re-run to verify the new delta, the spot price has changed and thus delta has changed... and the model that the system is based on isn't even exact anyway. And that's fine since in real life no options trader is going to waste their time trying to get the 100% perfect hedge for their book. As long as it's close to the desired delta, that's good enough.
Pricing and risk systems that banks and floor traders use are generally based on black scholes with customizations for the specific characteristics of the market in question, such as custom volatility surface which is updated many times a day and adjustments for changes in volatility prior to key relevant scheduled events/announcements. If the market price is not matching the black scholes price usually the reason is that the vol surface is stale or wrong. And even an up-to-date vol surface will be mostly interpolated from a few reliable points, so the models are never perfect. But when the vols are fresh these models are very close.
Sit recusandae velit ut. Et possimus fuga minima magnam. Nostrum voluptas exercitationem sit nisi numquam aliquid.
Pariatur nihil earum eum enim voluptatem voluptatem. Omnis consequatur est esse quos laudantium nihil ea pariatur. Eius est consequuntur consectetur dolore.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...