Questions tagged [delta-hedging]

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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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2 votes
1 answer
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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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Is this the PnL you would expect to see for a hedged call option portfolio? [closed]

You are a market maker. Charging no commission, your only aim is to remain market (delta) neutral. Therefore you construct a portfolio of the form: $$\Pi = -C - w_{1} B + w_{2} S$$ where $B = K \cdot ...
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Gamma/Convexity of a Swap vs a similar bond

As a rule of thumb, how would the duration and convexity of a 30y UST bond paying X% compare to the duration and convexity of a matched maturity vanilla interest rate swap, with a similar fixed rate. ...
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5 votes
1 answer
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Hedging strategy for payoff $\int_0^T\log S_u\mathrm{d}u$

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+\...
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1 vote
2 answers
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Delta hedging for an American call option on a stock with a continuous dividend yield

Let the dividend yield be $\delta$ and $C_u, C_d$ and $S_u, S_d$ be the up and down values for the stock and the call respectively over the period $\Delta t$. In Hull and all other resources I've ...
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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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Implementing a replicating strategy from the order book

So I have futures data in an order book (one screenshot every day at 12 p.m. for one month) for various futures products (i.e. various delivery periods such as the next day, the day after and so on) ...
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Path dependency for Delta hedge value

This is actually a follow-up questions for the two threads below - value of a delta hedged option: Delta hedge value formula Continuous delta hedge formula My question is that how the drift (mu) ...
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Why is a Delta-hedged option always profitable even in case of a sharp drop of value of the underlying?

I am trying to understand the following concept on a practical level. Given a Delta-hedged long call position, so holding a portfolio $$ Port_0 = C(S_0, \sigma) - \Delta_C(S_0) \, S_0 $$ If there is a ...
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Delta neutrality (derivation)

I'm confused about the math for the delta-neutral portfolio. Assume we have a short position in a European call option with price $p(t,S_t)$ and want to hedge it with the stock with price $S_t$. The ...
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Hedging in the Heston Model

I have simulated an underlying stock price, $S_t$ and a stochastic variance process, $v_t$ with the following stochastic differential equations from the Heston Universe: $$ dS_t = \mu S_tdt + \sqrt{...
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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 ...
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When you are delta-hedging by using shares, what is used? FIFO or LIFO? (Natenberg example)

When delta-hedging and using shares to do so, which "accounting" method should one use via their brokerage when they are executing the said delta-hedging adjustments? FIFO (first-in-first-...
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Quantity of risk-free asset in Black Scholes model

When the seller of a Call option hedges themselves, we know that they should buy $\Delta(t) = \mathcal{N}(d_1(t))$ amounts of the risky asset at time $t$. But what about the riskless asset? My ...
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Option seller: Why is delta hedging required if I am long/short the underlying with same number of lots as the OTM options I sold?

Situation: Sold OTM call while long the underlying. Stock did not tank, it went up too much breaching the breakeven point (strike price+premium). If I sell 1 lot of call options and I am being long ...
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Hedging or Relative Value Strategies with Rho or Tau Correlations?

I understand that the Pearson correlation indicates the strength of linear relationship between two data sets. The applicability of this to hedging strategies is intuitive: If I can establish a linear ...
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2 votes
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How can Ito's Lemma be used to show that a delta-neutral portfolio is instantaneously risk-free?

The lecture notes I am currently reading give the following example of a delta-neutral portfolio: minus one derivative (whose value at time $t$, when the value of the underlying is $S_t$, is denoted $...
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