Questions tagged [delta-hedging]

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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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1answer
178 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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64 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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81 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
380 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
66 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
70 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
102 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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140 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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38 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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29 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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1answer
128 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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1answer
38 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 ...
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1answer
163 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
138 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
123 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
69 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
157 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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61 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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99 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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60 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
292 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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1answer
145 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
173 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
296 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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111 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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92 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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101 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 ...
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1answer
164 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
470 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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79 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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86 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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56 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
440 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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38 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 ...
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1answer
262 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
170 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
129 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
121 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
160 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
611 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 ...
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1answer
79 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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2answers
79 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-...
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2answers
583 views

where does the cost of delta hedging come from?

I am reading John Hull's book, and am a bit confused about the explanation regarding the cost of delta hedging. Here is the background: a financial institute is selling call options with strike price ...
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132 views

Delta Forward and Put Call Parity

Vanilla options are traded interbank with delta hedge. The instrument employed to a delta hedge is usually a forward with the same expiry (and opposite delta) as the option. This means that in effect ...
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1answer
367 views

Expected Delta hedging frequency as function of implied (and realized) volatility

I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as ...
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2answers
444 views

What is "swimming delta" as a risk attribute in pnl explain?

What is swimming delta as in risk attribution?
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1answer
140 views

Is it possible to construct a hedge that matches value Delta Gamma and Vega?

Given a strike price, current price, risk free rate, dividend yield and volatility, I have been asked to calculate: - a hedge which matches the value Delta and Gamma - a hedge which matches the value ...
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1answer
75 views

Can a delta hedge be negative for all values at one time, and positive for all values at another time?

I have a problem that states there was a formula for the hedge $\delta(t, S_t)$ for a contingent claim whose value depends on only the stock value when $T=20$. In this hedge, $\delta(t, S_t)<0$ at $...