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BSM replication with expiry delta

I’ve been thinking about this problem and I’m missing something. Assuming a BSM world, I sell an OTM option at strike K. I then proceed to delta hedge it at the strike K each time K is touched. Why ...
Filippo's user avatar
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How to hedge an options portfolio in hft settings?

Suppose that you are quoting multiple option strikes on multiple levels and getting hit very often. Such trading possesses a challenge from a risk management perspective. To stay delta neutral you ...
Artem Korol's user avatar
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1 answer
127 views

Is price really the cost of hedging?

Assume a vanilla option with 1y expiry. The total vol in 1yr is 20 bps, the vol in first 6 months is 5 bps. The price is created by BS(20 bps). But is this price the correct cost of hedging? Will I ...
Arshdeep's user avatar
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stdev of delta hedged portfolio for call option !=0. Why?

I wrote a Monte-Carlo simulation of delta hedging for a european call. R and Sigma are fixed. I start simulation with zero money and short call option. At each step I borrow money to buy 'delta' of ...
lkjldfkjhljk's user avatar
1 vote
1 answer
138 views

P/L table for a delta hedged position

I am trying to replicate the table at pag. 119 of Dynamic Hedging by N. Taleb with no success. In the example called "A misleading delta" an operator has the following position: long \$1 ...
Enrico's user avatar
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How does delta adjustment relate to skew stickiness ratio (SSR)?

The correct delta hedging of a derivative $V$ in a model where volatility $\sigma$ is a function of the underlier $S$ requires a stock holding of an amount $$ \frac{dV}{dS}=\frac{\partial V}{\partial ...
Mr Frog's user avatar
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Synthetic replication of a spread option payoff

I have two assets, $S_1$ and $S_2$, and a European exchange-one-asset-for-another call option, such as those introduced by Margrabe (1978). So my payoff at expiration is the difference between the ...
Lisa Ann's user avatar
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Price display of weighted spreads via PCA and value changed

Using PCA I have the below PC1, first component weights, for 4 quarterly expiries of short term interest rate future. These are hypothetical values used to help my question. March: 0.005542604, June: ...
ChairmanMeow's user avatar
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1 answer
131 views

What to predict in delta-gamma hedging?

I am working in delta-gamma hedging with machine learning. I guess I have to predict gamma (since predicting gamma tells you how delta will behave) but I don't know why is it needed. I think that a ...
Kilkik's user avatar
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1 answer
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About delta basics [closed]

I am new to hedging and would like to work on delta-gamma hedging. However, I still have a lot of basic questions that are unclear to me. Suppose we hold a long call option with strike $K$, with ...
askersker's user avatar
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Precisely how do you delta-hedge a spot-1Y SOFR IRS with SOFR futures?

I'm struggling to construct hedge ratios that delta-hedge a spot-1Y IRS. Say I'm roughly in the middle of an IMM period, date = Oct 30th 2023 and I trade a 1k dv01 spot-1Y SOFR swap. I'll need some ...
User27's user avatar
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Constructing a monthly option from quarterly options and monthly futures

Say we have quarterly options and monthly futures where the strike price is based on the average price of spot during the corresponding period. There are no monthly options. Can I effectively ...
Sigma's user avatar
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1 answer
245 views

Hedging gamma, theta or other risks

Speaking on a high level, in the Black-Scholes model the $f\left(T,S_{T}\right)$ payoff's value dynamic is given by $$df\left(t,S_{t}\right)=\left(\frac{\partial f}{\partial t}\left(t,S_{t}\right)+\...
Kapes Mate's user avatar
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2 answers
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Buying a delta hedged payer swaption

If I/Client buy a European payer swaption, I understand that I gives me the right to pay the fixed rate at the strike level at maturity and receive a floating rate with an IRS- I expect interest rates ...
anon123SA12's user avatar
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Plotting net delta of calls and puts

I'm plotting the Net Delta of calls and puts for a given ticker symbol and a user specified range of expiration dates. Net Delta is calculated for each option contract using the following formula: <...
reknirt's user avatar
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Hedging exotic options

How can exotic and other path dependent, such as asian options be hedged? For example in the case of an asian option, what is the replicating portfolio: what instruments to keep in it and “how much”? ...
Kapes Mate's user avatar
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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 =...
Coco Garazzo's user avatar
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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 ...
Mathstudent123's user avatar
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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 ...
Frank's user avatar
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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 ...
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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 ...
poglhar's user avatar
1 vote
2 answers
597 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 ...
Tuo's user avatar
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0 answers
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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 ...
user2843539's user avatar
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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. ...
Slugger's user avatar
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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. ...
user1414512's user avatar
6 votes
0 answers
343 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 ...
Landscape's user avatar
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2 votes
1 answer
430 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 ...
helloimgeorgia's user avatar
2 votes
0 answers
106 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 ...
Wiles01's user avatar
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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 ...
Rodrigo's user avatar
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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 ...
Juan's user avatar
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2 answers
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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 ...
user avatar
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1 answer
456 views

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} > \...
Oliver Mohr Bonometti's user avatar
1 vote
1 answer
2k 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 ...
JamesSmith12's user avatar
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0 answers
103 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 ...
Samarth's user avatar
0 votes
1 answer
156 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 ...
Hasek's user avatar
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1 answer
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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 ...
user25844's user avatar
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2 votes
1 answer
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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 ...
Michael Grossmann's user avatar
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0 answers
136 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 ...
user121416's user avatar
1 vote
1 answer
485 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 ...
dan martin's user avatar
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0 answers
235 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 ...
lukas kiss's user avatar
3 votes
1 answer
694 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 ...
fwd_T's user avatar
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2 votes
2 answers
222 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{\...
PedroCazorla's user avatar
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0 answers
87 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 ...
Joe Shmo's user avatar
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1 answer
190 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 ...
barbatos233's user avatar
1 vote
1 answer
412 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 ...
Fadmad's user avatar
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4 votes
1 answer
222 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 ...
AlRacoon's user avatar
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228 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 ...
Maxime Willemet's user avatar
6 votes
3 answers
3k 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 ...
actinidia's user avatar
  • 196
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1 answer
220 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 ...
Rahul Jain's user avatar
1 vote
1 answer
228 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 ...
Sekots Reivan's user avatar

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