Questions tagged [delta-hedging]
The delta-hedging tag has no usage guidance.
186
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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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116 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)? ...
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1answer
131 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 ...
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82 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 ...
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1answer
101 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.
...
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124 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 ...
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107 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? ...
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74 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 ...
4
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1answer
190 views
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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66 views
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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133 views
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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2answers
594 views
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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1answer
108 views
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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1answer
90 views
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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2answers
126 views
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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2answers
163 views
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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39 views
Delta hedge analysis - volatility rapidly growing
I'm working with a hedge expirement design, where I daily hedge with EGARCH(1,1) forecasted volatilty based on a moving evaluation of the past 126 days.
However, I can't seem to understand the profit ...
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32 views
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:
$$ Z_t = \...
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197 views
A decent model to calculate hedges
Is there an option pricing model that wouldn't be too time consuming to set up in Python (for example) and that would provide better delta hedges than Black-Scholes? This would be mainly for equity ...
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46 views
Confused in regards to calculation of delta of one share including one call and one put [closed]
Q:My investment portfolio has one share of one call and one put, what would be the delta of my portfolio ?
delta of call:0.45
delta of put: -0.14
My thought process:
To begin with since im dealing ...
2
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1answer
181 views
For what options does the "delta hedging rule" apply?
I'm reading Shreve's Stochastic Calculus for Finance, Volume II. In chapter 4, he derives the "delta hedging rule":
$$\Delta(t) = c_x(t, S(t)) \text{ for all } t \in [0, T)\text{.}\tag{1}$$
...
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1answer
165 views
Delta hedge error black-scholes by Mark Davis
I'm currently reading a paper by Mark Davis in which he talks about a delta hedging error in the Black-Scholes formula.
The delta hedging error is given expressed as $Z_t$ with the formula:
$$Z_t = \...
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1answer
133 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 ...
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1answer
71 views
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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1answer
217 views
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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69 views
Equities Market Making Hedging, and Hedging Against the Effects of Hedging?
I was hoping someone could enlighten me as to how equity option market makers hedge in general, and whether they account for the effects of their purchases on the underlying share price when hedging ...
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107 views
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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67 views
Exercise on Delta-Neutal-Hedging
Suppose you have three positions in the following assets in euros: long on 10.000 calls (maturity T = 3 months, strike= 0.55, Delta (1 call) =0.533), short on 210000 calls (maturity T = 3 months, ...
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1answer
376 views
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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162 views
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,
$$\int_0^T\log S_u\mathrm{d}u=\int_0^t\log S_u\mathrm{d}u+\...
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2answers
200 views
Delta hedging for an American call option on a stock with a continuous dividend yield
Let the dividend yield be $\delta$ and $C_u, C_d$ and $S_u, S_d$ be the up and down values for the stock and the call respectively over the period $\Delta t$.
In Hull and all other resources I've ...
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4answers
394 views
Confusion about Vega P/L
For someone who has a delta hedged options position, the $\Gamma:= \frac{\partial^2V}{\partial S^2}$ roughly quantifies the amount of money made or lost if $$\frac{1}{\Delta t}\frac{(\Delta S)^2}{S^2} ...
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123 views
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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129 views
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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111 views
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 ...
2
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1answer
188 views
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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1answer
561 views
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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85 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 ...
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101 views
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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57 views
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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2answers
488 views
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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0answers
40 views
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 ...
2
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1answer
286 views
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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1answer
187 views
Question about using Ito's lemma in Gamma PnL
While deriving the delta hedge error if we hedge with implied vol, and the true vol is different, we say that the PnL of the call option is:
$$dC=C_tdt+C_SdS+0.5C_{ss}<QV>dt - (1)$$
Where $<...
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1answer
153 views
Why do replicating strategies delta hedge?
We have a simple BS-market of one risky asset $S_{t}$, a bond $B_{t}$ and a digital option $X$ on the risky asset with value process $V(t,S_{t})$. I was able to derive $V(t,S_{t})$ using risk-neutral ...
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1answer
125 views
Why my delta position is increasing with increase in spot?
I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and ...
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1answer
180 views
Long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma
I was reading a lot about the idea that long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma. But I couldn't understand why. In "Bunds and Bund ...
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1answer
839 views
Is there any way to check my delta hedging is implemented correctly?
When implementing a Black-Scholes delta-neutral portfolio using Python to perform delta hedging, I am not sure whether I implemented it correctly or not.
Unlike coding binomial trees for European ...
2
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1answer
85 views
Can a portfolio value consisting of longing a delta shares of stocks and shorting a call option greater than strike price?
While trying to implement Black-Scholes delta hedging for a European call option using Python, I came across the following phenomena:
Given a portfolio consisting of longing a delta shares of ...
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93 views
Binomial model and delta hedging
I've got a question about theory which is probably a one line answer. I use to understand it but I'm stuck right now.
In the Binomial model, we define the progression of the price as:
$$
S_k = S_{k-...
