# Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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### Dollar gamma formula and its derivation

I am seeing two formulas: $gamma = 0.5 * gamma * (stock price ^ 2)$gamma = gamma * (stock price ^ 2) Not sure where this 0.5 term is coming from. And also, what is the correct definition of ...
45 views

### The relationship btwn RV-IV and realized skew

In studying skew I've been advised to focus on understanding on components that affect it. One such component that's been recommended to me is the relationship btwn RV-IV and realized skew. ...
219 views

### How do we hedge option vega practically?

Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
1 vote
90 views

### local volatility not reasonable

We are going to generate synthetic option prices using a Heston model, i.e., $$\begin{gather*} dS_t = \sqrt{v_t} S_t dZ_t,\\ dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t, \end{gather*}$$ ...
198 views

### Should you compute the greeks on realized or implied volatility?

I am reading Trading Volatility by Collin Bennett and he says that you should compute the Greeks using realized volatility rather than implied volatility? Is this actually true? As far as I know the ...
35 views

### Hedging rates exposure in an FX options book

Fx options have exposure to the interest rates in the domestic and foreign currency. This risk can be hedged using currency forwards. In an ideal world, I suppose the best way would be to hold ...
1 vote
388 views

86 views

### Valuation of chooser options

The below formula for valuation of chooser options from Hull's book is not making sense to me. Why do we use call value at time T=0 while we use put value using t=0 call value and discount strike and ...
118 views

### Confusion with the equity option skew

In general out of the money (OTM) equity options have higher implied volatility (IV) than at the money (ATM) options. So assuming we have two put options (5% OTM and 10% OTM). Skew reveals that 10% ...
59 views

### Is there a financial instrument that is exposed to the change in growth of an asset over time?

Is there a financial instrument that is exposed to the rate of change of the value of a specific asset? If I believe a stock price will continue to grow in the future, but grow more slowly than in the ...
110 views

### Numerical scheme for this HJB equation

Without dwelling on details on how to obtain the HJB equation for this problem, I would like to know if the scheme I wrote for solving it numerically is viable or did I miss something. I need to solve ...