Questions tagged [delta-hedging]

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14
votes
1answer
415 views

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 ...
10
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2answers
2k views

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 ...
10
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3answers
10k views

Delta of binary option

What is the Delta of an at-the-money binary option with a payo out $0$ at $<100$ dollars, and payout $1$ at $>100$ dollars, as it approaches expiry? This is from a sample interview exam. I ...
10
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2answers
18k views

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 ...
10
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3answers
3k views

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 ...
10
votes
1answer
3k 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 ...
8
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3answers
2k 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 $S$...
8
votes
1answer
965 views

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 =...
7
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1answer
1k 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 ...
7
votes
1answer
303 views

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 + \...
6
votes
2answers
623 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 ...
6
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0answers
981 views

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-...
5
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1answer
7k 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 ...
4
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2answers
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 ...
4
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1answer
4k views

Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
4
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2answers
965 views

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 ...
4
votes
1answer
170 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 ...
4
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1answer
85 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?
3
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2answers
190 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 ...
3
votes
3answers
434 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 ...
3
votes
2answers
662 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 ...
3
votes
2answers
5k views

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 ...
3
votes
2answers
1k views

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 ...
3
votes
2answers
561 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. ...
3
votes
1answer
1k views

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 ...
3
votes
2answers
3k views

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 ...
3
votes
1answer
256 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 ...
3
votes
1answer
214 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 ...
3
votes
2answers
4k 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 ...
3
votes
1answer
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 ...
3
votes
1answer
571 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 ...
3
votes
0answers
89 views

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 ...
3
votes
0answers
1k views

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 ...
3
votes
0answers
131 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 ...
2
votes
1answer
161 views

The role of Gamma in replicating a put

I am analyzing portfolio protection by replication of a put. Having my portfolio with value $V$ I could buy put giving me the payoff $P$ resulting in a call like pay-off scenario $C=V+P$. Say, I don'...
2
votes
2answers
877 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 ...
2
votes
3answers
175 views

Why don't we take the differential to the Delta in the Delta hedge-portfolio

For option $V(S,t)$ with underlying asset $S$, we have a hedge portfolio $$\Pi = V(S,t) - \Delta(S,t)S$$ I always confuse here, when we take the differential of $\Pi$ $$d\Pi = dV -\Delta dS$$ why ...
2
votes
1answer
110 views

Why are vanilla OTC options are quoted in delta and vol?

Why do we quote options in delta bid-ask & volatility bid-ask & why not it is quoted in terms of option premium?
2
votes
1answer
53 views

duration hedging of illiquid bonds

Let's say that I have a totally illiquid 30Y bond that I want to hedge with short-dated bonds and that the market is liquid up to 10Y bonds. After 20 years, my 30Y bond will become a 10Y bond so I'll ...
2
votes
1answer
63 views

Change in call price Value as time goes by

In various papers and discussions in here I have seen that in delta hedging setup people compute the Change in value/Price of Call option by: $$ dC_t = \Theta_t dt + \Delta_t dS + \frac{1}{2} \...
2
votes
1answer
426 views

How to compute delta and delta-hedge in practice?

I keep hearing things like \begin{align*} ``\text{Traders make their book delta-neutral at the end of each trading day''} \end{align*} I am wondering what this means, and why this is supposed to give ...
2
votes
2answers
151 views

$E[F_T] = F_0 \ \rightarrow \ \text{or} \ \leftarrow \ p = \frac{1-d}{u-d}$?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to Chapter 16 and 17,...
2
votes
3answers
424 views

Tracking error Black Scholes

Suppose an asset follows the SDE $$ d S_{t}^{1} = \mu S_{t}^{1} dt + \sigma_{t} S_{t}^{1} d W_{t} $$ Furthermore assume that $r = 0$ and a trader who uses Black-Scholes for pricing and hedging with ...
2
votes
1answer
335 views

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 ...
2
votes
1answer
78 views

A bug in delta hedging, when for a certain step dS=0

Suppose we are doing a delta hedging simulation according to Black Scholes, where the initial condition are [stockPrice, strike, timeToExpire ,riskFreeRate, dividend, sigma, isCall] = [100, 100, 1, 0, ...
2
votes
1answer
353 views

Justification for Binary Option's Infinite Delta?

First time poster here. Glad to be here. I just graduated with an MSc in computational finance. I recently read a question by another user about the delta of an at-the-money binary option as it ...
2
votes
2answers
136 views

Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma \sigma}b^2(\sigma)+\frac{...
2
votes
1answer
283 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest $p_t+\Delta_t*S_t>...
2
votes
1answer
107 views

Profit and Loss on delta-hedged portfolio

The overnight profit formula from a textbook (possibly Derivative Markets by McDonald) is the following: $$\Delta _{t}(S_{t+h}-S_{t})-(V_{t+h}-V_{t})-(e^{rh}-1)(\Delta_{t}S_{t}-V_{t}),$$ where Delta ...
2
votes
1answer
210 views

Traders view on hedging of FX Futures with FX Forward

I would like to get a trades view on hedging a FX Forward with a FX Future by just moving the (1) FX_Spot rate and ignore the other risk factors (2) ccy1 DV01 risk, (3) ccy2 DV01 risk, (4) basis swap ...