Questions tagged [delta-hedging]
The delta-hedging tag has no usage guidance.
0
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1answer
30 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} $ ...
2
votes
0answers
30 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 ...
1
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0answers
49 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, ...
0
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0answers
56 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?
1
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2answers
152 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)]...
2
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1answer
67 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
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1answer
46 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
votes
1answer
72 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?
1
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0answers
36 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 ...
0
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2answers
253 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$ ...
0
votes
1answer
69 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 ...
4
votes
2answers
274 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 ...
1
vote
1answer
108 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.
...
2
votes
1answer
56 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} \...
3
votes
2answers
304 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 ...
0
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1answer
162 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:
$$C(t)=(S(t)-K)\Phi(\frac{S(t)-K}{\sigma \sqrt{T-t}})+\sigma \sqrt{T-t} \phi(\frac{S(t)-...
3
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0answers
48 views
Computing Malliavin Derivative for European Call Payoff
Let $X_t$ be a continuous local-martingale modeling the stock price given by
$$
X_t = \int_0^t \sigma_t(T,K)dW_t
,
$$
and $\sigma_t(T,K)$ is an $L^2$-measurable process not adapted to $W_t$'s ...
0
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0answers
39 views
Delta of a Digital option [duplicate]
A digital option with a Stock as the underlying pays 1 if the stock price at maturity is above the strike $S_T>k$ and it pays nothing otherwise.
I have computed the value proces to be following:
$$...
6
votes
1answer
132 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 + \...
5
votes
3answers
1k 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$...
4
votes
1answer
109 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 ...
0
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0answers
177 views
Question about Delta Hedging
So in Delta Hedging, we know that the delta value gives us the hedge ratio between the option and the stock. For example, if we are long 10 shares of stock, and the delta value is 0.5, then we would ...
-3
votes
1answer
155 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 ...
3
votes
0answers
39 views
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 (...
3
votes
1answer
153 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 ...
2
votes
0answers
341 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 ...
1
vote
0answers
765 views
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 ...
2
votes
1answer
278 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} $$
Furthermore assume that $r = 0$ and a trader who uses Black-Scholes for pricing and hedging with ...
5
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0answers
469 views
Gamma Imbalance / Exposure
I am currently writing my thesis about the lack of volatility / changing market structure we see nowadays on the financial market. I believe an important factor in this development is the delta-...
3
votes
2answers
702 views
Delta Hedging with fixed Implied Volatility to get rid of vega?
I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day.
I've read this post but would like different information :
Delta Hedging with fixed Implied Volatility ...
2
votes
3answers
152 views
Why don't we take the differential to the Delta in the Delta hedge-portfolio
For option $V(S,t)$ with underlying asset $S$, we have a hedge portfolio
$$\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 ...
0
votes
2answers
523 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 ...
3
votes
3answers
319 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 ...
-1
votes
1answer
282 views
Delta Hedging: Clarification example of the book “Hull, Options, Futures, and Other Derivatives” [closed]
By "Hull, Options, Futures, and Other Derivatives":
Suppose that, in figure,the stock price is \$100 and the option price
is \$10. Imagine an investor who has sold 20 call option
...
0
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0answers
39 views
Can discretization of delta hedging give negative profits?
If we long a call and short delta the underlying, and then discretely update the hedge, we expect to profit if realized volatility is greater than implied volatility.
However, since we are doing ...
0
votes
1answer
373 views
Example of delta one products
Not sure if this is the right place to ask such question.
How close to 1 should the delta be in order for the product to be classified as delta one.
2.What examples of delta one products are there?
7
votes
1answer
851 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 ...
3
votes
1answer
70 views
Delta-hedging non-volatile stock
If a stock has zero vol and some positive drift $\alpha$ (in a BS-setting) and we delta hedge a long call option dynamically over a year with some positive implied volatility.... how would that work ...
6
votes
1answer
4k 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 ...
3
votes
1answer
209 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
315 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 ...
3
votes
1answer
203 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
0answers
46 views
Reference for delta hedging programmatically
I learned some of the basic theory of Bjork (chap 1-9)
and would now like to study some (discrete delta) hedging using programming software.
We had an exercise in school where we hedged a call ...
-1
votes
4answers
88 views
What is the effect of increasing volume depth to stock volatility? [closed]
Say, an investment bank want to hedge its Long Gamma position on its Long Call option by placing limit orders in the exchange.
Limit orders result in increasing volume depth.
Empirically, what is the ...
3
votes
1answer
205 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)? ...
1
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0answers
170 views
Risk management for Digital Option at large Bank
Say, an investment bank sell Digital Call Option to its client at strike 100.
But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&...
3
votes
0answers
726 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
77 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, ...
1
vote
3answers
79 views
Computation of limit
In Delta of binary option,
I do not see how to prove that the limit of $\partial C_t/\partial S_t$ is equal to $+\infty$ as $t \rightarrow T$. Can someone help ?
14
votes
1answer
348 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 ...
