# Tagged Questions

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### Hedging - calculating option prices using implied volatility surface

To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding ...
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### Delta Hedge, does large stock move produce a loss?

I dont understand how MM protect themselves from large moves in underlying while being delta hedged. Example: MM sels 1 ATM put and sells 100stock (delta = 1) as a hedge. Now what will happen if next ...
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### Delta Hedging for 2 Factor Models

If the value of an option at Maturity is what is the off-setting position you take for X and Y, if you are i)Long Call of the option ii)Short Call of the option iii)Long Put of the option iv)Short ...
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### How do market makers hedge VIX index options?

With equity options, many market makers hedge by buying or selling the underlying asset in correspondence with the option's delta. For example, if the market maker wrote 1 call option with a delta of ...
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### $E[F_T] = F_0 \ \rightarrow \ \text{or} \ \leftarrow \ p = \frac{1-d}{u-d}$?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to ...
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### Delta of binary option

What is the Delta of an at-the-money binary option with a payo out $0$ at $<100$ dollars, and payout $1$ at $>100$ dollars, as it approaches expiry? This is from a sample interview exam. I ...
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### delta hedging strategy for OTM option

Wondering how you would think about the following thought experiment - suppose you sell an OTM call option and plan to implement a delta hedging strategy whereby if the price of the stock were to ...
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### How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
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### Delta hedging Question [closed]

What is the delta of a short position in 1,000 European call options on silver futures? The options mature in eight months, and the futures contract underlying the option matures in nine months. The ...
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### Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
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### Delta Hedging with fixed Implied Volatility or floating Implied Volatility?

When delta hedging an option until expiry at implied volatility, is it better to rehedge using the fixed implied volatility given by the option price upon its purchase (or sale), or to rehedge using ...
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### Initial holdings of bonds with delta hedging (Black Scholes model)

Consider the Black Scholes model so $$dS_t = \mu S_t dt + \sigma S_t dW_t, \;\;\; dB_t = rB_t dt$$ I want to delta hedge an European call option with strike price $K$ and strike time $T$. It is known ...
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### derivation of the hedging error in a black scholes setup

I'm reading the following short paper by Davis. In section 2.6 he wants to derive an expression for the hedging error. Assume we have Black scholes setup: $$dS_t = S_t(r dt + \sigma dW_t)$$  dB_t =...
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### Delta hedging cost of exotic options?

I'm simulating dynamic delta hedging for up-and-out call option. For plain vanilla call options, I heard that the option price is the expected value of the accumulated delta hedging cost. Does it also ...
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### Practical Delta hedging under stochastic volatility models (e.g. SABR model)

I'm currently straggling with Delta hedging under SABR model (or other stochastic volatility models). As far as I know there are numerous Delta hedging strategies theoretically and practically such as ...
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### Why is this delta-hedging/P&L example on a variance swap call correct?

I'm looking into this article about var swaps: http://sbossu.com/docs/VarSwaps.pdf and not sure how to correctly interpret Exhibit 2.1.1. "In this example an option trader sold a 1-year call ...
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### Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma \sigma}b^2(\sigma)+\frac{...
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### The role of Gamma in replicating a put

I am analyzing portfolio protection by replication of a put. Having my portfolio with value $V$ I could buy put giving me the payoff $P$ resulting in a call like pay-off scenario $C=V+P$. Say, I don'...
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### How to manage risk on a call calendar when underlying is falling

Let us say I bough a call calendar spread. Now, at expiry of the short option, the underlying has decreased significantly, and I am approaching my max loss(i.e both the options are close to 0). In ...
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### Delta-Gamma Neutral portfolio, derivation issue

Let $C$ be an option on an underlying $S$. I want to construct a portfolio $V$ using another asset $C_0$ such that the delta and the gamma of $V$ is the same as the delta/gamma of $C$, in order to ...
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### Under what circumstances would one want to delta hedge a straddle

Under what circumstances would one want to delta hedge a straddle option? This link explains: ...
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### How to hedge a long stock with the corresponding volatility ETF

Let us say I want to establish a market neutral position. So if I buy 50 shares of stock (SPY) and I want to delta hedge, I sell an ATM covered call. So that brings the position delta to 0. Now, I ...
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What does it mean to implement a delta-neutral strategy for straddle ? A straddle consists in buying a call and a put simultaneously, at the same date, on same underlying, with same maturity and ...
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### Delta hedging frequency for plain vanilla European options under trading costs

I am looking for methods to select points in time when delta hedging plain vanilla European options under trading costs. It is easy to come up with ad hoc ideas such as Time-based: for example at ...
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### Mock/practice trading for options (delta/gamma hedging etc.)

I know there are some sites for practicing equity investing. But could you provide me with suggestions concerning options trading etc. I read Natenbergs book on Options and want to test things like ...
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### Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
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### Zakamouline Optimal Hedging of Options with Transaction Costs

I've read that the Zakamouline method suggests the best optimal hedging of options when taking transaction costs into account. I've read the article but am having difficulty understanding it well ...
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### Is it wrong to use 'real world' probabilities for option valuation?

Is it wrong to use 'real world' probabilities for option valuation, even when the market is not liquid enough to delta hedge the option? My instinct is that it is wrong, because the time value of ...
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### Breakeven of a delta-hedged option

Basic question to which I surprisingly did not find an answer on here. What's the best approximation to the break-even (with respect to stock price) for an option that was hedged fully at point of ...
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### backtesting options strategies in R

I would like to backtest an options strategy in R. I require the ability to delta hedge and rebalance to options in the portfolio at different frequencies (daily, monthly,etc.) What packages are the ...