Questions tagged [delta-hedging]
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23
questions
1
vote
2answers
425 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 ...
3
votes
3answers
669 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 ...
14
votes
2answers
3k 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 ...
12
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4answers
18k views
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....
6
votes
1answer
10k 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 ...
8
votes
1answer
1k 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 =...
13
votes
3answers
7k 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$...
0
votes
2answers
1k views
Dynamic Delta Hedging And a Self Financing Portfolio
Let's assume the usual Black Scholes assumptions hold. My question is related to an answer on this question. There, the weights ($\Delta_t^1$,$\Delta_t^2$) are derived which form a locally risk free ...
7
votes
1answer
6k views
Effect of volatility on the delta of a call option
In the book 'Dynamic Hedging', Nassim Taleb writes:
...
4
votes
1answer
210 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?
10
votes
1answer
4k 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 ...
6
votes
2answers
2k 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
2answers
2k 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
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 ...
3
votes
3answers
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 ...
1
vote
1answer
2k 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)-...
4
votes
0answers
2k 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 ...
1
vote
1answer
1k 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.
...
3
votes
2answers
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. ...
2
votes
2answers
201 views
$E[F_T] = F_0$ implies $p = \frac{1-d}{u-d}$? or is implied by?
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
1answer
404 views
Pricing and Hedging an Option through a Currency Triangle
How is the option price of an plain vanilla option (in a Black Scholes setting) derived, which is written on, say XAGGBP but practically hedged with XAGUSD and GBPUSD (because these are more liquid)? ...
2
votes
3answers
216 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 ...
1
vote
1answer
105 views
How to manage risk on a call calendar when underlying is falling
Let us say I bough a call calendar spread. Now, at expiry of the short option, the underlying has decreased significantly, and I am approaching my max loss(i.e both the options are close to 0).
In ...