Questions tagged [delta-hedging]
The delta-hedging tag has no usage guidance.
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Hedging option delta
Let's say I am long 1000 50 delta call options. I need to hedge my deltas now. There can be infinite ways to do this. How should I think about proceeding wit this? My first thought was, if the ...
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24 views
Hedged portfolio dynamics under T-forward measure
I'm looking to find the hedging PDE for a multi-currency derivative $u(F_d, F_f, X,t, T)$ under the T-forward measure, using the delta-hedging argument (F - forward rate, X - forward FX rate).
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51 views
Delta Hedging Example
I was reading Dynamic Hedging by N. Taleb and in the chapter dedicated to the delta, there is this example of a trader position in options (one-month European call, flat yield curve, forward is ...
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1answer
101 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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FX option trading [duplicate]
Are all trades quoted in implied vol terms 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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1answer
50 views
European Call option replication
An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time.
I use a Monte Carlo algorithm to ...
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1answer
81 views
Delta hedging: theoretical value vs actual price
One way to derive the Black-Scholes PDE is via the Delta-hedging argument:
Suppose that $V_t = V(t, S_t)$, for some function $V: [0,T] \times \mathbb{R} \to \mathbb{R}$. We construct a portfolio by ...
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46 views
Simple 3 way delta hedge
Consider 3 futures contracts:
A BTC/ETH, settled in BTC
B USD/ETH, settled in ETH
C USD/BTC, settled in BTC
As the markets aren't efficient, sometimes these ...
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51 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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64 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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61 views
Variance swap = delta hedged strip of options
Is there a paper that explicitly shows/demonstrates that a variance swap can be replicated by delta-hedging a strip of options?
Thus far I have not found anything: papers mention it in passing ...
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60 views
FX Spot Delta market standard calculation (Trader View)
I am just writing my thesis about FX instrument and hedging and one question popped up which I can't solve. Maybe it is silly but cant find anything about it how the delta of a fx spot is defined and ...
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58 views
In literature, is IV constantly adjusted during option delta hedging?
In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under ...
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1answer
96 views
Market Maker ETF Hedging Strategy
Some thoughts about ETF hedging; feel free to leave comments!
Scenario 1:
An investor sells 1M ETF shares to a Market Maker(MM) at bid price. MM has a long position and will need to offload the ...
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1answer
97 views
Why does it make sense to delta hedge a deep OTM option given the very low delta exposure? [closed]
I am not sure if this is actually done in practice as I'm not a derivatives trader, but I can only think of reducing the cost of the OTM option as a reason for delta hedging a deep OTM option, which ...
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47 views
Books and techniques to hedge options that expire tomorrow?
Can anyone point me to books or resources that talk about best techniques to hedge ATM or close to ATM options that expire tomorrow. I am particularly interested on how to hedge if you are short the ...
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66 views
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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1answer
123 views
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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46 views
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
141 views
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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38 views
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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191 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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208 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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3answers
312 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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1answer
217 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 ...
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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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84 views
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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46 views
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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78 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
373 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
210 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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42 views
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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59 views
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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127 views
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
479 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
153 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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2answers
272 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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1answer
204 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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121 views
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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3answers
231 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
124 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?
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1answer
56 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 ...
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1answer
94 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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79 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
620 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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237 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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259 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
67 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
803 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 ...
