# Tag Info

Accepted

### Delta-Hedging Exotic Options

Consider reading Lorenzo Bergomi's excellent book -- or at least the first chapter available here for download --, it will help you clarify things. Some remarks as to your original question: It is ...
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### delta-hedging is failing

Regarding your 1st question, jumps are indeed unhedgeable. From a theoretical point of view, you might want to look at Merton's "Option pricing when underlying stock returns are discontinuous", the ...
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### What really is Gamma scalping?

Gamma scalping (being long gamma and re-hedging your delta) is inherently profitable because you make 0.5 x Gamma x Move^2 across the move from your option. (You get shorter delta on downmoves, so you ...
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### What really is Gamma scalping?

Assuming all else remains equal (implied vol has not changed and very little time decay has occurred), Gamma scalping can best be explained by Gamma (or realized volatility) enhancing the value of a ...
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### When should we delta hedge?

By delta hedging you are saying that you have a view on the path and the volatility of the option you are trading, but not on its direction; in your case, that being short delta. From a theoretical ...
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### Derivation of BS PDE problem using Delta hedging

This question has been asked many times and some clarifications appear needed. As pointed out in an answer to this question, the portfolio \begin{align*} \Delta_t^1 S_t + \Delta^2_t C, \end{align*} ...
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### Effect of Implied volatility on option delta

In the Black-Scholes-Merton model, with model option price $V$ as a function of underlying price $S_t$, strike price $X$, continuously compounded risk-free rate $r$, continuously compounded dividend ...
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### Proof of gamma profit formula

Assume you buy a plain vanilla call option at the price $V$ and the spot $S$. You immediately delta hedge buy selling $\partial V / \partial S$ units of the underlying asset. The underlying asset now ...
• 6,084
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### Dynamic Delta Hedging And a Self Financing Portfolio

Main references As explained in my comments, the correct approach to derive the hedging portfolio would be the one described in Gordon's answers to the following questions: Derivation of BS PDE ...
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### What really is Gamma scalping?

As long as you live in a world where implied and realized vol are the same, there is no net profit (or loss) from gamma scalping. However, if they are different, then you make a gain or loss which is ...
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Yes, in the sense that it is assumed that the delta will be passed between participants at time of execution. Not necessarily. A non delta neutral trade may be used for speculation , or for hedging.
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### Hedging strategy for payoff $\int_0^T\log S_u\mathrm{d}u$

I assume you want to price a derivative product that pays $\int_0^T\ln S_tdt$ at maturity time $T$, from time $t=0$. I'll ignore generalization to time $t$ because it is trivial (split the integral in ...
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### Delta Hedging with fixed Implied Volatility to get rid of vega?

You should have a look at the following paper: Ahmad, Riaz and Paul Wilmott (2005) "Which free lunch would you like today, Sir? Delta hedging, volatility arbitrage and optimal portfolios," Wilmott ...
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### What is the effect of increasing volume depth to stock volatility?

Answers to your 3 questions: Empirically, there is no effect. I understand that this is not logical but it is reality. Adding thickness to an order book does not necessarily make it harder or easier ...
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### Dynamic Delta Hedging And a Self Financing Portfolio

for a self financing portfolio, you have a holding in stocks and one in bonds. If we want to do a hedging simulation, at the start of each step, work out the total value of the hedger's holding (...
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### Derivation of BS PDE problem using Delta hedging

this is the d on the delta problem. (In my book concepts I discuss this. Sections 5.6 and 5.7 ) Essentially we hold delta constant across time steps and so ignore the d on the delta because there is ...
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### Delta Hedging: Clarification example of the book "Hull, Options, Futures, and Other Derivatives"

We denote by $C(S_0, K)$ the price for a call option with payoff $(S_T-K)^+$ at the option maturity $T.$ Here $S_0=100$ is the spot stock price. Generally, \begin{align*} C(S_0, K) \ne (S_0-K)^+. \...
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### Example of delta one products

As indicated by the name, delta one products have a delta of exactly 1 (at least theoretically) with respect to the underlying; moreover, AFAIK the delta has to be constant, i.e. a product with ...
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### Basic practical question about Delta hedging

As has been remarked in the comments already, the standard deviation of your hedging error should approach zero as your re-hedging frequency (the number of time steps) increases. Here is a sample ...
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