# Questions tagged [delta-hedging]

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### Delta-Hedging Exotic Options

I have already figured out that Delta-hedging essentially turns European options into volatility products where you pay implied vol and get paid realized vol for long positions and you pay realized ...
521 views

### How to, from various hypotheses on the P&L, get known models (BS, Heston etc ...)

Usually models in quantitative finance are taught by giving, let's say, stochastic differential equations, initial conditions, and then pricing, under the model, various derivatives written on the ...
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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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### What really is Gamma scalping?

How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price $V(t,S)$ at time $t$ and the underlying stock price at $S$...
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### Delta of binary option

What is the Delta of an at-the-money binary option with a payout $0$ at $S(T)<100$ dollars, and payout of $1$ at $S(T)>100$ dollars, as it approaches expiry? This is from a sample interview exam....
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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 ...
4k views

### 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 ...
2k views

### delta-hedging is failing

and thank you for answering me ! While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them. First, I thought that the implementation was ...
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### Gamma Imbalance / Exposure

I am currently writing my thesis about the lack of volatility / changing market structure we see nowadays on the financial market. I believe an important factor in this development is the delta-...
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### Proof of gamma profit formula

http://www.volcube.com/resources/options-articles/gamma-hedging-trading-strategies-part-i/ I would like to have proven to me the above formula, mostly because I don't quite understand it. The formula ...
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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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### Interpertation of delta hedge error in Black Scholes

I have spent some time to prove the delta hedge error as described in this paper paper page 16-17 by Davis. The proof is discussed here Deriving Delta Hedge error in the B-S setup (part 2) (a post by ...
147 views

What would a hedging strategy look like for a payoff $\int_0^T\log S_u\mathrm{d}u$? I have determined under Black-Scholes stock dynamics, $$\int_0^T\log S_u\mathrm{d}u=\int_0^t\log S_u\mathrm{d}u+\... 2answers 479 views ### Expected value of delta-hedged portfolio Consider portfolio in black-scholes world \Pi = \Delta S - V, where S is the stock price and V is the price of the option. I have read that if we set \Delta = \frac{\partial V}{\partial S}  ... 2answers 6k views ### Delta Neutral / Gamma Neutral Positions I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ... 2answers 2k views ### Why doesn't a simulated delta hedging process go to zero? I put together a simple simulation of delta hedging a set of options with an underlying and it seems that the fluctuations of the price still seem to affect the final outcome. The reason, I understand ... 4answers 315 views ### Confusion about Vega P/L For someone who has a delta hedged options position, the \Gamma:= \frac{\partial^2V}{\partial S^2} roughly quantifies the amount of money made or lost if$$\frac{1}{\Delta t}\frac{(\Delta S)^2}{S^2} ...
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Are all FX trades ( RR, BF, ATM)quoted in implied vol term delta neutral trades? If trades are not delta neutral at the initiation does that mean it is speculative trading? Why/ why not?
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### Delta Hedging with fixed Implied Volatility to get rid of vega?

I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day. I've read this post but would like different information : Delta Hedging with fixed Implied Volatility ...
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### Why does volatility increase the expense of delta-hedging?

Consider someone that writes a call, and wishes to delta-hedge against it to remain delta neutral. For this to be profitable, the price they sell this option for should be greater than or equal to the ...
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When we derive the P&L of a delta hedged option we obtain: $$\text{P&L}=\dfrac{1}{2}\Gamma(\delta S)^{2}-\theta\delta t$$ and setting equal to zero and rearranging we obtain: $$\dfrac{1}{... 1answer 529 views ### Option order imbalance Currently studying the paper: HU, Jianfeng. Does Option Trading Convey Stock Price Information?. (2014). Journal of Financial Economics. 111, (3), 625-645. Research Collection Lee Kong Chian School ... 1answer 129 views ### Using BS Delta to hedge in a LV Model Why do some people use a Black Scholes Delta instead of the delta given by the Local Volatility model? 0answers 2k views ### How does P&L of delta hedged option position accumulate over time? Assume that I long ATM Call option on a stock at 20% implied volatility. This Call option will expire in 1 month. If, over this coming month, the underlying moves with 30% volatility and I delta-hedge ... 2answers 744 views ### When should we delta hedge? Let's say I'm the seller of a European call option on a non-dividend paying stock. I pocket the premium c_0 of the call at t=0. If I start to delta-hedge right away, this is equivalent to ... 3answers 669 views ### Derivation of BS PDE problem using Delta hedging I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of (S,t) we have, due to Ito's lemma, that: \begin{eqnarray*} dC = \left(\frac{\partial C}{\partial ... 2answers 2k views ### Gamma/delta dynamics in the Black Scholes model and it's relation to PnL (Basic of option theory) If we are in a Black Scholes setup and a I have a Call option and hedged it by shorting delta amount of its underlying. What does the second derivative of the call with respect to Price of the ... 2answers 595 views ### where does the cost of delta hedging come from? I am reading John Hull's book, and am a bit confused about the explanation regarding the cost of delta hedging. Here is the background: a financial institute is selling call options with strike price ... 2answers 1k views ### Why/How does a hedged portfolio make profits? This is probably a very easy question but I am new to the field and couldn't find an answer. Assuming that I am building a hedged portfolio with a long option and going short delta on the underlying. ... 1answer 1k views ### 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 struck ... 3answers 3k views ### 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 ... 1answer 127 views ### Correlation for Trading vs. Risk Management Assume a portfolio that contains some asset A and that I am contemplating hedging my delta in A by taking a position in asset B. I would determine how much of B to buy/sell based on the linear ... 1answer 493 views ### Basic practical question about Delta hedging I am trying to understand a simple thing about Delta hedging in the Black-Scholes world. I know I'm doing something blatantly wrong, I just can't see it now. Let's say I write a call option and sell ... 1answer 524 views ### Floating Strike Lookback Delta Risk I'm running through some delta hedging simulations of floating strike lookback call options (that is, I'm short the options) during a volatile (downside) period for the underlying and some very odd ... 1answer 1k views ### Hedging a binary option close to expiry I have been asked to prove mathematically that a binary option close to maturity should be hedged using a call spread with the same maturity. I understand that far from maturity, one would use delta ... 2answers 6k views ### hedging barrier options Consider Black Scholes dynamics for the stock price$$dS_t=\mu S_tdt+\sigma S_t dW_t$$I have "heard" it is difficult hedging barrier options if the payoff suddenly is set to zero by the boundary ... 1answer 2k views ### 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 ... 1answer 605 views ### 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 ... 0answers 88 views ### Delta hedging the day before expiry In practice, how do people usually delta hedge options the day before expiry? Would you still use the black Scholes delta and then close out the position in the underlying immediately after expiry? ... 0answers 80 views ### How often to tune the regularisation parameter in LASSO? I'm trying to implement the following paper: Avellaneda & Lee (2010), Statistical Arbitrage in the US equities market. To build the strategy, the idea is to trade a stock and hedge using a basket ... 1answer 376 views ### Expected Delta hedging frequency as function of implied (and realized) volatility I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as ... 0answers 114 views ### Uniqueness of the Hedging strategy I am currently reading the book "Nonlinear Option Pricing" by Julien Guyon. In the book they defined an attainable payoff F_T as a \mathcal{F}_T measurable random variable for which there exists ... 0answers 145 views ### 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 ... 2answers 1k views ### 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 ... 3answers 216 views ### Why don't we take the differential to the Delta in the Delta hedge-portfolio For option V(S,t) with underlying asset S, we have a hedge portfolio$$\Pi = V(S,t) - \Delta(S,t)S$$I always confuse here, when we take the differential of \Pi$$d\Pi = dV -\Delta dS why ...
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'...