Questions tagged [delta-hedging]
The delta-hedging tag has no usage guidance.
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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 ...
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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 ...
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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 ...
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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 ...
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How to simulate a delta hedged option strategy
I'd like to do a montecarlo simulation of a $\Delta$ hedged strategy (long OTM call) to see how the PnL distributes on cases like:
$\sigma_{bought} < \sigma_{realized}$
$\sigma_{bought} > \...
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How to actually compute delta when delta hedging with a (time varying) volatility model?
I was reading some papers on delta hedging, many of which reference "Which Free Lunch Would You Like Today, Sir?" (Ahmad/Wilmott) which describes the following setup:
Quote option with $\...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Stress scenarios for Down In Put (DIP)
I am preparing stress scenarios for long Down In Puts (e.g -10%,-15% drop in underlying equity price). I assume that the maximum delta hedge is 300% for DIPs with barrier levels within 0%-5% ...
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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 ...
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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{\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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)? ...
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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 ...
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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 ...
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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.
...
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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 ...
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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? ...
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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 ...
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Delta hedge swaption straddle
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 ...
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Effect of Implied volatility on option delta
I am currently hedging a short put option where strike is 6027 and expiry is 30th Mar 2023. As per my understanding when option is ITM increase in volatility will decrease the delta and decrease in ...
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Barrier shift consideration in delta hedging down and in puts (PDI)?
I have a question regarding the barrier shift used when risk managing a down and in put (PDI). I'm reading Exotic Options Trading by Frans de Weert and he gave this example.
Trader is long one PDI 100/...
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Gamma-neutral delta-neutral call ratio spread
I have been looking into options strategies that minimize risk via delta neutrality. One such strategy seems to be the gamma-neutral delta-neutral call ratio spread, in which the gamma is neutralized ...
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Best/worst case scenario after selling OTM call option
You decide to sell a European call option that is currently 10% OTM (for example the strike = 100 and the current price = 90). You have to delta hedge to keep the delta of your position at 0.
What is ...
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Implementing a hedging strategy for oil future options
I am currently writing a paper examining two models for pricing options on WTI Crude oil futures, and I want to backtest hedging strategies from both model and compare them against each other.
However,...
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Empircal data analysis delta hedge error of Black-Scholes by Mark Davis
Regarding Mark Davis derivation of the delta-hedging error occuring in the black-scholes as a result of difference in realized volatility and implied volatily. The formula reads as follows:
$$ Z_t = \...
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A decent model to calculate hedges
Is there an option pricing model that wouldn't be too time consuming to set up in Python (for example) and that would provide better delta hedges than Black-Scholes? This would be mainly for equity ...
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Confused in regards to calculation of delta of one share including one call and one put [closed]
Q:My investment portfolio has one share of one call and one put, what would be the delta of my portfolio ?
delta of call:0.45
delta of put: -0.14
My thought process:
To begin with since im dealing ...
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For what options does the "delta hedging rule" apply?
I'm reading Shreve's Stochastic Calculus for Finance, Volume II. In chapter 4, he derives the "delta hedging rule":
$$\Delta(t) = c_x(t, S(t)) \text{ for all } t \in [0, T)\text{.}\tag{1}$$
...
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Delta hedge error black-scholes by Mark Davis
I'm currently reading a paper by Mark Davis in which he talks about a delta hedging error in the Black-Scholes formula.
The delta hedging error is given expressed as $Z_t$ with the formula:
$$Z_t = \...
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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 ...
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Dumb Question: Delta-Neutral fractional shares [closed]
If neutralizing delta requires an addition of a fractional number of shares, e.g. 444.12345 do we generally keep the decimals or round up to the nearest integer? I reckon rounding would no longer ...
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How do you finance theta decay when replicating an option?
When constructing a replicating portfolio for a short position in a call option under Black Scholes, I am not able to pinpoint the source of gains from theta decay. When theta decay materializes, I ...
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