# Questions tagged [delta-hedging]

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### Delta Gamma Hedging Portfolio of Multiple Options Derivation

I am trying to make the correct derivation of the Delta Gamma Hedge of a portfolio composed of a multi-option strategy, like a Straddle with the following parameters Long 1 Call K = 100, Long 1 Put K =...
75 views

### Delta hedge for derivative in Black-Scholes market

Consider a derivative in the Black-Scholes market with the price formula $\Pi_t = F(t,S_t)$. I want to find a self-financing portfolio consisting of the stock and the bank account that hedges the ...
76 views

### What would be the practitioner way of hedging jump risks?

I have developed a keen interest in volatility strategies and have implemented various approaches based on practitioner delta. This delta is meticulously calibrated using a no-arbitrage implied ...
136 views

### At what threshold on delta percentage should I hedge my option portfolio?

I am able to identify and build an option portfolio with long/short call/put options across different strikes and expiries such that the gamma is positive and cost is negative. Upon inception I hedge ...
73 views

### Question regarding delta-hedging principle

A delta-hedging principle involves taking the opposite direction, i.e., short and long, to hedge against financial risk. An example is longing an option call and selling (shorting) the borrowed the ...
1 vote
448 views

### Cost of Delta Hedging

I am confused about the following question: A trader holds a portfolio of short option positions. The trader limits the risk of these exposures by maintaining a delta hedging strategy. In evaluating ...
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### Compute Forward Variance Swap

I'm trying to compute a forward variance like this paper https://arxiv.org/pdf/2105.04073.pdf. The paper shows that under rough stochastic volatility model assumption, options can be hedged with the ...
49 views

### Where am I going wrong with the calculation of conitnuous PnL from delta hedging?

I am trying to work out the PnL of continuous delta hedging. I saw This link to an answer here, however, I obtained a different answer without resorting to Black Scholes, which I will outline below. ...
247 views

### Is a volatility forecast essentially a delta forecast in vanilla European options?

As the title suggests. I want to understand why delta hedging is done. I'd like to illustrate with an example: Say you have 7 dte option chain with 15.8% IV ATM straddle on an underlying of spot 100. ...
298 views

### Delta-hedge experiment of American Put option

I am trying to run a delta-hedge experiment for an American Put option but there's a (systematic) hedge error which I cannot seem to understand or fix. My implementation is found in the bottom of this ...
276 views

### Optimal delta-hedging frequency when gamma scalping

Is there a practical way to calculate a delta threshold for rebalancing when gamma scalping? I know it does not effect expected P&L, but what about optimizing for P&L sharpe ratio after ...
100 views

### Exact delta-hedging for endogenous payoffs

I would like to derive the exact delta-hedging strategy in the Black-Scholes market to replicate the following non-standard endogenous payoff. The particularity is that the payoff does not only depend ...
1 vote
227 views

### How do banks and dealers effectively hedge a variance swap?

It is known that a variance swap can be replicated by a strip of options. However, it is costly to trade that many OTM options and there is not enough liquidity to trade the wings in the quantity that ...
851 views

### Delta-Gamma neutral vs Delta-Vega neutral

Imagine that the underlying stock price is 110. The call option has a strike price of 100. The annualized volatility is 25% and the interest rate is 10%. Finally, the time to maturity is 0.5 years. We ...
960 views

### Delta-hedging frequency directly affects PnL, and not just PnL smoothness and variance?

The information I have found about delta hedging frequency and (gamma) PnL on this site and numerous others all reiterate the same thing: that the frequency at which you delta-hedge only has an effect ... 272 views

1 vote
1k views

### Calculating the PnL of a delta-hedged option at a point in time

In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final expected PnL based on implied ...
45 views

### Does using borrowed capital make a Uniswap liquidity position hedged from impermanent loss

According to the following article, using borrowed capital can make a Uniswap position delta neutral. https://lambert-guillaume.medium.com/how-to-deploy-delta-neutral-liquidity-in-uniswap-or-why-euler-...
64 views

### Sticky Strike vs Sticky Delta - revisited [duplicate]

Given a time series of implied volatility smiles over the last 100 days for a given option (e.g. 1y S&P call, or 1y x 10y swaption), and the corresponding forward rates, what test should be ...
84 views

### Representing a continuous time hedge discretely

I recently came across an example (Section 5.2.9 here) which does a simple delta hedging experiment. Below are the details: Market conditions Interest rates are at a 2% level --> r = 0.02 The ...
142 views

### How do sell-side institutions manage interest rate derivatives books in practice?

I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such ...
196 views

### Delta of a forward ATM option

Reading: What are some useful approximations to the Black-Scholes formula? I understand that a ATM Call option can be approximated to $$C(S,t)≈0.4Se^{−r(T−t)}σ \sqrt{T−t}$$ Also, I often hear that an ...
120 views

### pros and cons of hedging oil contracts with options or futures

I work for an oil trading company. We sell petroleum products indexed on the Brent and hedge our fixed price sales using futures to offset price fluctuations. We do not engage in speculation. I was ...
119 views

### How do you explain consistently making money with discrete hedging a call option?

In a backtest I did, I'm selling a call option and buying a delta amount of the underlying (calculated using implied vol). Now I know in the limit case of continuous hedging I end up paying a PnL ...
1 vote
381 views

### Delta hedging when volatility is stochastic

From my understanding in a BSM world you can make a bet on volatility using options and delta hedging with the underlying. If you think realized volatility of the underlying will be higher than the ...
196 views

### black Scholes model hedging without constant volatility

I have started to look deeply in the hedging and I have created some simulations to simulate delta hedging strategies. I use BS model to calculate delta. The only issue was, which Volatility should I ...
472 views

### Gamma squeeze - mathematical explanation

I am trying to understand from a mathematical and financial point of view the mechanism behind the so-called gamma squeeze. Is there a good source to read about this/ My questions are: what are the ...
202 views

### Black-Scholes PDE derivation gap

Most derivations of the Black-Scholes formula end up with the following dynamics of some (hedged) portfolio:  \int_{t=0}^{T} \left(\frac{\partial f}{\partial \tau}(S(t),t)+\frac{1}{2}\cdot\frac{\...
84 views

### Option's Delta Investopedia Question

New to this. In this Investopedia article on Delta the following looks like a typo - How Do Options Traders Use Delta? Delta is used by options traders in several ways. First, it tells them their ...
150 views

### Negative-gamma delta hedging (for a call option writer): how will the stock price affect the portfolio profit?

Suppose a (European) call option writer is hedging their risk by taking a long position in stocks (holding $\delta_C$ shares). The value of the portfolio is $V(S)=\delta_CS-C$. Then is the gamma of ...
1 vote
262 views

### Computing Delta-Hedged Option Returns

I was reading some papers on delta-hedged option returns and came across an intriguing paper that I found quite interesting. However, I was a bit confused on the authors' methodology of computing ...
217 views

### When does the underlying become the derivative?

Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does ...
174 views

### Option P&L over time

I would like to compute the evolution of the P&L of an FX plain vanilla option. Unfortunately, I am not sure about the correctness of my reasoning. Let's imagine that I sell a 1W call option on a ...
2k 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 ...
183 views

### Can I Delta hedge Swaption with 1month option expiry on 10 year swap as 1 month forward starting swap (expiry 10 yr) & notional as Delta% of swaption [closed]

Whether below is correct 1 month expiry of swaption with 10 year swap underlying can be delta hedged as with below swap: Notional of swap = delta% of swaption multiplied by notional of swaption As of ...
1 vote
190 views

### Delta Hedging with a Different Underlying

In Bouzoubaa and Osseiran page 68 equation 5.3, the authors discuss delta hedging a call written for asset $S_1$ using a different but correlated underlying asset $S_2$. The authors provide the ...
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### Does delta hedging mimic the disposition effect?

A friend of mine sent me a no-name paper on the disposition effect yesterday and asked for my opinion about it. Therein, the authors claim to have detected some evidence for a strong disposition ...
1 vote
292 views

### at what frequency do option market makers delta hedge

Could someone with option market making experience tell me usually at what frequency do the major option market makers delta-hedge their positions (say for US single stocks or equity indices)? ...
311 views

### Caplet delta hedging

I have had a really hard time trying to simulate the delta hedging of a caplet. When I compare the process to delta hedging a call on a stock (which I already did without much trouble), I found some ...
240 views

### Questions during reading option volatility and pricing from Sheldon Natenberg

This question comes from the book of Sheldon Natenberg's book "Option Volatility and Pricing: Advanced Trading Strategies" 2nd. In chapter 8 "Dynamic Hedging" page 129, it says: In ...
747 views

### Delta hedging error in B-S (hedging with implied vol) question

I have been thinking about this for a while and am at my wits end. Now assume I am pricing a call at implied vol $s$, whereas the realized volatility is $σ$. Let $C$ be the incorrect pricing function. ...
315 views

### Confusion Regarding Dynamically Delta Hedging a Short Option

To my understanding, market makers (mm) in the options market dynamically delta-hedge their portfolios by buying/shorting the underlying, thus eliminating directional risk and profiting from providing ...
183 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? ...
84 views

### General question regarding delta heding

I was wondering if I have to take the strike prices of options into consideration when doing a gamma and delta hedging. As an example, let's suppose that I have 2 positions: a long position call ...
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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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### profit opportunities from accurate forecasting of delta?

Are there any option trading strategies that can profit by modeling delta more accurately than Black-Sholes does? I'm looking at models for predicting delta, and I can clearly see how these can help ...
1k views

Let's say you decide to buy a 2Y10Y ATM swaption straddle (i.e. buy 10 million ATM payer swaption and buy 10 million ATM receiver swaption). In order to delta hedge, I believe you would short the ...
1 vote