Questions tagged [delta-hedging]

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Delta-Hedging Exotic Options

I have already figured out that Delta-hedging essentially turns European options into volatility products where you pay implied vol and get paid realized vol for long positions and you pay realized ...
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14 votes
3 answers
8k views

What really is Gamma scalping?

How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price $V(t,S)$ at time $t$ and the underlying stock price at $S$...
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How to, from various hypotheses on the P&L, get known models (BS, Heston etc ...)

Usually models in quantitative finance are taught by giving, let's say, stochastic differential equations, initial conditions, and then pricing, under the model, various derivatives written on the ...
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13 votes
4 answers
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Delta of binary option

What is the Delta of an at-the-money binary option with a payout $0$ at $S(T)<100$ dollars, and payout of $1$ at $S(T)>100$ dollars, as it approaches expiry? This is from a sample interview exam....
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2 answers
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How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
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12 votes
3 answers
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Delta hedging frequency for plain vanilla European options under trading costs

I am looking for methods to select points in time when delta hedging plain vanilla European options under trading costs. It is easy to come up with ad hoc ideas such as Time-based: for example at ...
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10 votes
1 answer
5k views

Delta Hedging with fixed Implied Volatility or floating Implied Volatility?

When delta hedging an option until expiry at implied volatility, is it better to rehedge using the fixed implied volatility given by the option price upon its purchase (or sale), or to rehedge using ...
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9 votes
1 answer
2k views

delta-hedging is failing

and thank you for answering me ! While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them. First, I thought that the implementation was ...
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8 votes
1 answer
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derivation of the hedging error in a black scholes setup

I'm reading the following short paper by Davis. In section 2.6 he wants to derive an expression for the hedging error. Assume we have Black scholes setup: $$ dS_t = S_t(r dt + \sigma dW_t)$$ $$ dB_t =...
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8 votes
1 answer
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Hedging error in a stochastic volatility model

I would like to find how much error I make when I hedge a call option using Black Scholes model in a market which is actually governed by a stochastic volatility process such as $$dS_t = rS_tdt + \...
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  • 595
7 votes
1 answer
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Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
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  • 1,354
7 votes
1 answer
11k views

Proof of gamma profit formula

http://www.volcube.com/resources/options-articles/gamma-hedging-trading-strategies-part-i/ I would like to have proven to me the above formula, mostly because I don't quite understand it. The formula ...
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  • 285
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0 answers
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Gamma Imbalance / Exposure

I am currently writing my thesis about the lack of volatility / changing market structure we see nowadays on the financial market. I believe an important factor in this development is the delta-...
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6 votes
2 answers
1k views

How do market makers hedge VIX index options?

With equity options, many market makers hedge by buying or selling the underlying asset in correspondence with the option's delta. For example, if the market maker wrote 1 call option with a delta of ...
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6 votes
2 answers
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Interpertation of delta hedge error in Black Scholes

I have spent some time to prove the delta hedge error as described in this paper paper page 16-17 by Davis. The proof is discussed here Deriving Delta Hedge error in the B-S setup (part 2) (a post by ...
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  • 1,585
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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5 votes
2 answers
585 views

Expected value of delta-hedged portfolio

Consider portfolio in black-scholes world $\Pi = \Delta S - V$, where $S$ is the stock price and V is the price of the option. I have read that if we set $\Delta = \frac{\partial V}{\partial S} $ ...
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  • 61
4 votes
3 answers
817 views

Derivation of BS PDE problem using Delta hedging

I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of $(S,t)$ we have, due to Ito's lemma, that: \begin{eqnarray*} dC = \left(\frac{\partial C}{\partial ...
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  • 921
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2 answers
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Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
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4 votes
2 answers
2k views

Why doesn't a simulated delta hedging process go to zero?

I put together a simple simulation of delta hedging a set of options with an underlying and it seems that the fluctuations of the price still seem to affect the final outcome. The reason, I understand ...
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4 votes
4 answers
662 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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4 votes
1 answer
259 views

FX option trading questions

Are all FX trades ( RR, BF, ATM)quoted in implied vol term delta neutral trades? If trades are not delta neutral at the initiation does that mean it is speculative trading? Why/ why not?
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  • 507
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2 answers
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Delta Hedging with fixed Implied Volatility to get rid of vega?

I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day. I've read this post but would like different information : Delta Hedging with fixed Implied Volatility ...
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  • 41
4 votes
1 answer
191 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 ...
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  • 5,325
4 votes
1 answer
214 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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4 votes
1 answer
3k views

Gamma PnL Formula and Break-Even volatility

When we derive the P&L of a delta hedged option we obtain: $$ \text{P&L}=\dfrac{1}{2}\Gamma(\delta S)^{2}-\theta\delta t $$ and setting equal to zero and rearranging we obtain: $$ \dfrac{1}{...
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  • 909
4 votes
1 answer
600 views

Option order imbalance

Currently studying the paper: HU, Jianfeng. Does Option Trading Convey Stock Price Information?. (2014). Journal of Financial Economics. 111, (3), 625-645. Research Collection Lee Kong Chian School ...
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  • 1,346
4 votes
1 answer
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Hedging a binary option close to expiry

I have been asked to prove mathematically that a binary option close to maturity should be hedged using a call spread with the same maturity. I understand that far from maturity, one would use delta ...
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4 votes
1 answer
392 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 ...
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  • 151
4 votes
1 answer
480 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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  • 2,046
4 votes
1 answer
142 views

Using BS Delta to hedge in a LV Model

Why do some people use a Black Scholes Delta instead of the delta given by the Local Volatility model?
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  • 2,161
4 votes
0 answers
125 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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  • 243
4 votes
0 answers
103 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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  • 83
4 votes
0 answers
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How does P&L of delta hedged option position accumulate over time?

Assume that I long ATM Call option on a stock at 20% implied volatility. This Call option will expire in 1 month. If, over this coming month, the underlying moves with 30% volatility and I delta-hedge ...
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3 votes
2 answers
894 views

When should we delta hedge?

Let's say I'm the seller of a European call option on a non-dividend paying stock. I pocket the premium $c_0$ of the call at $t=0$. If I start to delta-hedge right away, this is equivalent to ...
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  • 489
3 votes
2 answers
2k views

Gamma/delta dynamics in the Black Scholes model and it's relation to PnL (Basic of option theory)

If we are in a Black Scholes setup and a I have a Call option and hedged it by shorting delta amount of its underlying. What does the second derivative of the call with respect to Price of the ...
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  • 127
3 votes
2 answers
752 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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3 votes
2 answers
1k views

Why/How does a hedged portfolio make profits?

This is probably a very easy question but I am new to the field and couldn't find an answer. Assuming that I am building a hedged portfolio with a long option and going short delta on the underlying. ...
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  • 31
3 votes
1 answer
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Why is this delta-hedging/P&L example on a variance swap call correct?

I'm looking into this article about var swaps: http://sbossu.com/docs/VarSwaps.pdf and not sure how to correctly interpret Exhibit 2.1.1. "In this example an option trader sold a 1-year call struck ...
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  • 31
3 votes
3 answers
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backtesting options strategies in R

I would like to backtest an options strategy in R. I require the ability to delta hedge and rebalance to options in the portfolio at different frequencies (daily, monthly,etc.) What packages are the ...
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3 votes
1 answer
151 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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3 votes
1 answer
533 views

Basic practical question about Delta hedging

I am trying to understand a simple thing about Delta hedging in the Black-Scholes world. I know I'm doing something blatantly wrong, I just can't see it now. Let's say I write a call option and sell ...
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  • 175
3 votes
1 answer
606 views

Floating Strike Lookback Delta Risk

I'm running through some delta hedging simulations of floating strike lookback call options (that is, I'm short the options) during a volatile (downside) period for the underlying and some very odd ...
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3 votes
2 answers
7k views

hedging barrier options

Consider Black Scholes dynamics for the stock price $$dS_t=\mu S_tdt+\sigma S_t dW_t$$ I have "heard" it is difficult hedging barrier options if the payoff suddenly is set to zero by the boundary ...
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  • 425
3 votes
1 answer
2k views

Breakeven of a delta-hedged option

Basic question to which I surprisingly did not find an answer on here. What's the best approximation to the break-even (with respect to stock price) for an option that was hedged fully at point of ...
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  • 190
3 votes
1 answer
614 views

Hedging - calculating option prices using implied volatility surface

To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding ...
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  • 219
3 votes
1 answer
336 views

Optimal Hedging of Options - asymmetry between long and short vol positions

Going over Zakamouline's Approximation method for optimal delta hedging of options, it is claimed that the result remains valid for both buying options (long vol positions) or selling options (short ...
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  • 103
3 votes
0 answers
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Uniqueness of the Hedging strategy

I am currently reading the book "Nonlinear Option Pricing" by Julien Guyon. In the book they defined an attainable payoff $F_T$ as a $\mathcal{F}_T$ measurable random variable for which there exists ...
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3 votes
0 answers
151 views

Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
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  • 131
2 votes
2 answers
1k views

Is it wrong to use 'real world' probabilities for option valuation?

Is it wrong to use 'real world' probabilities for option valuation, even when the market is not liquid enough to delta hedge the option? My instinct is that it is wrong, because the time value of ...
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