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Questions tagged [delta-hedging]

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transactions costs and leland modified volatility

When there are transactions costs, we are in a situation of incomplete market. What does the modified volatility of Leland (Option Pricing and Replication with Transactions Costs, 1985) bring us? can ...
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61 views

Derivative of the Black and Scholes equation [on hold]

What is the financial interpretation that the derivative of the Black and Scholes equation is equal to 0? St n(d1) - Xe^-rt n(d2) = 0
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Delta hedging theta pnl

Say I sell a swaption and delta hedge it, and the breakeven daily move in the underlying is $x$ bps. Then if on any given day the actual move in the underlying is $y$ bps $( y <x)$. Then I, as ...
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How should one hedge option positions on the date of expiry?

Let's say we are looking at a non-liquid equity ticker and a slightly OOM option on it. The problem is that if we buy delta to hedge it, it could move the underlying market and push the option to be ...
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3answers
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Delta hedging pnl to recover option price

In Black Scholes framework, assuming zero interest rates and realized volatility to be same as implied volatility, gamma pnl is exactly same and opposite of theta pnl. So if I buy an option and delta ...
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Understanding delta based strike selection in an Iron Condor

I am reading a small book on the proper use of Iron Condors (link). I do not use these strategies as I have had a very hard time being profitable on them. This book mentions some strategies to ...
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73 views

Implied volatility as break-even delta hedge volatility

There have been some posts on this topic, but not what I am looking for, so a new post on an old topic.. I think some/most of us here are familiar with the following formula expressing implied ...
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2answers
185 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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147 views

Options Delta Meaning of Term [closed]

not able to understand delta in options. Whilst I understand, it is how much the option moves when the underlying moves by 1 unit, I fail to understand, when someone books a currency option, why does ...
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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 ...
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85 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 ...
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Break-even volatility for delta hedge portfolio

After simulating practical and theoretical PnL of a delta hedged portfolio on some data from the SPX500 under 0.15 management Vol I want to find the Vol which gives me an accumulated PnL of 0. ...
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Correct beta weighted delta options formula?

Is this the correct formula for beta weighted delta: http://www.nishatrades.com/blog/beta-weighted-delta I've seen this What is the formula for beta weighted delta and gamma? but they seem to be ...
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57 views

replicate option by dynamic hedging

I've just started working for a company with a decent commodity exposure. They manage this by as they call it dynamically hedging it. Basically when they start the hedging they identify a market ...
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2answers
326 views

why gamma decreases when option is deep in the money? [closed]

Gamma decreases when a call option goes either deeper in, or deeper out of the money. That is due the demand for the call option. I can imagine the demand for the option would decrease as it goes ...
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1answer
146 views

Delta hedging/Gamma PnL

Suppose I am long USDIDR straddle with my start of the day delta being USD10m long IDR and USDIDR gamma being $5m. There is a 1% intra-day IDR strengthening, so my delta becomes roughly long IDR 15m....
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Confused by Solution to the Expected Profit when Hedging an option using Implied Volatility (from Wilmott 2006)

Paul Wilmott on Quantitative Finance 2nd Ed (section 12.5.1) gives a solution to the initial expected profit when hedging using delta based on implied volatility as $$\frac{1}{2}(σ^2 - σ̃^2) \,\int_{...
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Effect of mean reverting Volatality in Black and Scholes? [closed]

Can someone please elaborate what would be the effect of a mean reverting volatility (instead of a constant volatility) in pricing options using BS ? Also how would the greeks vary?
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How is the performance measure computed here?

The image is from John C Hull Textbook titled Options, Futures and Other Derivatives ( page 407 - Ninth Edition). The table above was obtained after computing the delta of stock price, shares ...
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2answers
332 views

Hedging with machine learning

I’ve been thinking about an interesting problem lately: Suppose I have a position in an exotic derivative. How can I automate the hedging process? Traditionally, one build a pricing model and ...
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1answer
124 views

How is FX cross rates options are priced?

Say I have market for EUR/USD and also USD/CAD, how would EUR/CAD would be priced and hedged in practice? What are good papers/book chapters to read on that? (Assuming basic knowledge already on ...
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1answer
179 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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159 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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Can prediction of realized volatility for next day improve delta hedging (gamma scalping)?

Im quite confused. As I understand from standard delta PNL of option + underlying position, pnl is equals to difference between realized and implied vol weighted by gamma. However, as I understood, ...
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59 views

Implied Volatility of a call plus its delta

I would like to understand if exists a smart way to imply the volatility from a quote that is the sum of a call and its delta: is there any method other than simple iterative minimization?
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2answers
187 views

Heging against stochastic interest rate

I am working on an Index and I am trying to price Call options on it. I work with the 3 Months LIBOR as Cash. I use the following Black-Scholes formula $$C_{t} = S_{t}e^{-q_{t}(T-t)}\mbox{N}[d_{1}(t)]...
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1answer
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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?
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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 ...
4
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1answer
83 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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74 views

Delta hedge a long option using a short option [closed]

If I long a call option of 1 mio USD/SGD for example, I understand that at strike price (ATM), delta is approximately +0.5. To approximately hedge this delta, I also understand we can short 0.5 mio ...
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2answers
512 views

How does a Delta Hedged portfolio yield the Risk-free?

Here I'm considering the simple case of a dealer writing call options on a stock and hedging the short position with a "textbook" Delta Hedge, i.e. goes long on $N_c \times Delta$ stocks (where $N_c$ ...
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1answer
207 views

Difference in exposure between delta hedged options, ATM straddles and delta hedged straddles

What is the difference in exposures between delta hedged options, ATM straddles and delta hedged straddles. They all seem to provide the same thing, which is exposure to volatility. What are the ...
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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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1answer
201 views

Deriving Delta Hedge error in the B-S setup (part 2)

In this paper paper page 16-19 by Davis and this discussion derivation of the hedging error in a black scholes setup, the derivation of the delta hedging error in the Black Scholes model is discussed. ...
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1answer
62 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} \...
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2answers
621 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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1answer
457 views

Bachelier model call: computation of delta of a call option

The price of a call with a stock with Bachellier process as its underlying and zero interest rate is giving by: $$C(t)=(S(t)-K)\Phi(\frac{S(t)-K}{\sigma \sqrt{T-t}})+\sigma \sqrt{T-t} \phi(\frac{S(t)-...
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Computing Malliavin Derivative for European Call Payoff

Let $X_t$ be a continuous local-martingale modeling the stock price given by $$ X_t = \int_0^t \sigma_t(T,K)dW_t , $$ and $\sigma_t(T,K)$ is an $L^2$-measurable process not adapted to $W_t$'s ...
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1answer
288 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 + \...
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3answers
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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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1answer
199 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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1answer
177 views

Can we 'predict' the delta of a stock? The delta of a stock is $\pm 1$ right? [closed]

“A stock is like a living organism. A sparrow, say. And we are able to create an emergent-based abstraction of that sparrow, which closely approximates the sparrow itself, accounting for migration ...
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Calculate latest underlying price (or option), given new option (or underlying) market price?

Given a reference underlying price, reference option price, delta and gamma, if I receive a new underlying/option price what equation should I use to calculate the respective option/underlying price (...
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1answer
201 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 ...
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0answers
533 views

Delta hedging vs Strangle

Long volatility delta hedging and strangle are common long volatility strategies. We can make strangle delta neutral(in $) by buying more puts than calls(if an absolute value of put delta is less than ...
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Short Call Hedge. Options and gamma trading

Let’s say a trader sells a Short Call with strike 100 (for making profit with the premium) at-the-money (for highest extrinsic value there). For hedging until expiration, he buys the underlying share ...
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3answers
402 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 ...
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883 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-...
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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 ...
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3answers
171 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 ...