Questions tagged [delta-hedging]
The delta-hedging tag has no usage guidance.
167
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Delta hedge error black-scholes by Mark Davis
I'm currently reading a paper by Mark Davis in which he talks about a delta hedging error in the Black-Scholes formula.
The delta hedging error is given expressed as $Z_t$ with the formula:
$$Z_t = \...
3
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1answer
98 views
Correlation for Trading vs. Risk Management
Assume a portfolio that contains some asset A and that I am contemplating hedging my delta in A by taking a position in asset B. I would determine how much of B to buy/sell based on the linear ...
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1answer
67 views
Dumb Question: Delta-Neutral fractional shares [closed]
If neutralizing delta requires an addition of a fractional number of shares, e.g. 444.12345 do we generally keep the decimals or round up to the nearest integer? I reckon rounding would no longer ...
2
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1answer
143 views
How do you finance theta decay when replicating an option?
When constructing a replicating portfolio for a short position in a call option under Black Scholes, I am not able to pinpoint the source of gains from theta decay. When theta decay materializes, I ...
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48 views
Equities Market Making Hedging, and Hedging Against the Effects of Hedging?
I was hoping someone could enlighten me as to how equity option market makers hedge in general, and whether they account for the effects of their purchases on the underlying share price when hedging ...
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90 views
Is this the PnL you would expect to see for a hedged call option portfolio? [closed]
You are a market maker.
Charging no commission, your only aim is to remain market (delta) neutral.
Therefore you construct a portfolio of the form:
$$\Pi = -C - w_{1} B + w_{2} S$$
where $B = K \cdot ...
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0answers
55 views
Exercise on Delta-Neutal-Hedging
Suppose you have three positions in the following assets in euros: long on 10.000 calls (maturity T = 3 months, strike= 0.55, Delta (1 call) =0.533), short on 210000 calls (maturity T = 3 months, ...
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1answer
115 views
Gamma/Convexity of a Swap vs a similar bond
As a rule of thumb, how would the duration and convexity of a 30y UST bond paying X% compare to the duration and convexity of a matched maturity vanilla interest rate swap, with a similar fixed rate.
...
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1answer
123 views
Hedging strategy for payoff $\int_0^T\log S_u\mathrm{d}u$
What would a hedging strategy look like for a payoff $\int_0^T\log S_u\mathrm{d}u$? I have determined under Black-Scholes stock dynamics,
$$\int_0^T\log S_u\mathrm{d}u=\int_0^t\log S_u\mathrm{d}u+\...
1
vote
2answers
104 views
Delta hedging for an American call option on a stock with a continuous dividend yield
Let the dividend yield be $\delta$ and $C_u, C_d$ and $S_u, S_d$ be the up and down values for the stock and the call respectively over the period $\Delta t$.
In Hull and all other resources I've ...
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4answers
187 views
Confusion about Vega P/L
For someone who has a delta hedged options position, the $\Gamma:= \frac{\partial^2V}{\partial S^2}$ roughly quantifies the amount of money made or lost if $$\frac{1}{\Delta t}\frac{(\Delta S)^2}{S^2} ...
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97 views
Implementing a replicating strategy from the order book
So I have futures data in an order book (one screenshot every day at 12 p.m. for one month) for various futures products (i.e. various delivery periods such as the next day, the day after and so on) ...
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0answers
46 views
Path dependency for Delta hedge value
This is actually a follow-up questions for the two threads below - value of a delta hedged option:
Delta hedge value formula
Continuous delta hedge formula
My question is that how the drift (mu) ...
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0answers
94 views
Why is a Delta-hedged option always profitable even in case of a sharp drop of value of the underlying?
I am trying to understand the following concept on a practical level.
Given a Delta-hedged long call position, so holding a portfolio
$$
Port_0 = C(S_0, \sigma) - \Delta_C(S_0) \, S_0
$$
If there is a ...
2
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1answer
119 views
Delta neutrality (derivation)
I'm confused about the math for the delta-neutral portfolio.
Assume we have a short position in a European call option with price $p(t,S_t)$ and want to hedge it with the stock with price $S_t$. The ...
0
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1answer
307 views
Hedging in the Heston Model
I have simulated an underlying stock price, $S_t$ and a stochastic variance process, $v_t$ with the following stochastic differential equations from the Heston Universe:
$$
dS_t = \mu S_tdt + \sqrt{...
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38 views
How to write the iterative procedure hedging with replicating method?
I'm trying to replicate the following delta hedging table from hull(10th ed, table 19.2):
Older ed How to understand this example from Hull's book?
...
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0answers
72 views
How often to tune the regularisation parameter in LASSO?
I'm trying to implement the following paper: Avellaneda & Lee (2010), Statistical Arbitrage in the US equities market.
To build the strategy, the idea is to trade a stock and hedge using a basket ...
0
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0answers
69 views
When you are delta-hedging by using shares, what is used? FIFO or LIFO? (Natenberg example)
When delta-hedging and using shares to do so, which "accounting" method should one use via their brokerage when they are executing the said delta-hedging adjustments? FIFO (first-in-first-...
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56 views
Quantity of risk-free asset in Black Scholes model
When the seller of a Call option hedges themselves, we know that they should buy $\Delta(t) = \mathcal{N}(d_1(t))$ amounts of the risky asset at time $t$.
But what about the riskless asset? My ...
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2answers
265 views
Option seller: Why is delta hedging required if I am long/short the underlying with same number of lots as the OTM options I sold?
Situation: Sold OTM call while long the underlying. Stock did not tank, it went up too much breaching the breakeven point (strike price+premium).
If I sell 1 lot of call options and I am being long ...
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0answers
24 views
Value in time of the bond in delta-hedging
I am trying to implement a simple delta-hedging strategy. The idea is that I want to verify that the covered position "1 option long + delta stocks short" is actually evolving as $e^{rt}$, ...
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36 views
Hedging or Relative Value Strategies with Rho or Tau Correlations?
I understand that the Pearson correlation indicates the strength of linear relationship between two data sets. The applicability of this to hedging strategies is intuitive: If I can establish a linear ...
2
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1answer
171 views
How can Ito's Lemma be used to show that a delta-neutral portfolio is instantaneously risk-free?
The lecture notes I am currently reading give the following example of a delta-neutral portfolio:
minus one derivative (whose value at time $t$, when the value of the underlying is $S_t$, is denoted $...
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1answer
148 views
Question about using Ito's lemma in Gamma PnL
While deriving the delta hedge error if we hedge with implied vol, and the true vol is different, we say that the PnL of the call option is:
$$dC=C_tdt+C_SdS+0.5C_{ss}<QV>dt - (1)$$
Where $<...
0
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1answer
109 views
Why do replicating strategies delta hedge?
We have a simple BS-market of one risky asset $S_{t}$, a bond $B_{t}$ and a digital option $X$ on the risky asset with value process $V(t,S_{t})$. I was able to derive $V(t,S_{t})$ using risk-neutral ...
1
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1answer
116 views
Why my delta position is increasing with increase in spot?
I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and ...
0
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1answer
119 views
Long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma
I was reading a lot about the idea that long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma. But I couldn't understand why. In "Bunds and Bund ...
2
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1answer
406 views
Is there any way to check my delta hedging is implemented correctly?
When implementing a Black-Scholes delta-neutral portfolio using Python to perform delta hedging, I am not sure whether I implemented it correctly or not.
Unlike coding binomial trees for European ...
2
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1answer
74 views
Can a portfolio value consisting of longing a delta shares of stocks and shorting a call option greater than strike price?
While trying to implement Black-Scholes delta hedging for a European call option using Python, I came across the following phenomena:
Given a portfolio consisting of longing a delta shares of ...
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2answers
60 views
Binomial model and delta hedging
I've got a question about theory which is probably a one line answer. I use to understand it but I'm stuck right now.
In the Binomial model, we define the progression of the price as:
$$
S_k = S_{k-...
2
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2answers
424 views
where does the cost of delta hedging come from?
I am reading John Hull's book, and am a bit confused about the explanation regarding the cost of delta hedging.
Here is the background: a financial institute is selling call options with strike price ...
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2answers
112 views
Delta Forward and Put Call Parity
Vanilla options are traded interbank with delta hedge. The instrument employed to a delta
hedge is usually a forward with the same expiry (and opposite delta) as the option. This means
that in effect ...
2
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1answer
265 views
Expected Delta hedging frequency as function of implied (and realized) volatility
I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as ...
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2answers
310 views
What is “swimming delta” as a risk attribute in pnl explain?
What is swimming delta as in risk attribution?
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1answer
134 views
Is it possible to construct a hedge that matches value Delta Gamma and Vega?
Given a strike price, current price, risk free rate, dividend yield and volatility, I have been asked to calculate:
- a hedge which matches the value Delta and Gamma
- a hedge which matches the value ...
1
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1answer
73 views
Can a delta hedge be negative for all values at one time, and positive for all values at another time?
I have a problem that states there was a formula for the hedge $\delta(t, S_t)$ for a contingent claim whose value depends on only the stock value when $T=20$. In this hedge, $\delta(t, S_t)<0$ at $...
1
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1answer
181 views
Hedging Interest rate swaps in practice
Suppose we have a portfolio of i terest rate swaps that we wish to delta hedge. we build a delta ladder by shocking the instruments used to build the forecasting and discouting curves (Eurodollar ...
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19 views
Synthetically sell to close puts in limited-margin IRA
Suppose:
I bought an American put on a stock in a retail brokerage IRA, where I can't sell short or write uncovered options.
The put is ITM and has served its purpose for hedging.
The put is thinly ...
0
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2answers
189 views
Delta Hedged PnL on Call Spread
Suppose I buy a call and then sell a call one dollar in strike higher. Suppose I get into this position for 10 cents lower than it is theoretically worth. (I.e if this spread is worth 0.50 I just ...
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1answer
111 views
Delta heding & PnL
Sorry if it's a duplicate but i didn't find an answer to my simple question in the other posts.
Let say we short a call option on a stock.
$K = 100$, $C = 1$, $S = 100$ and $\Delta = 0.5$. No ...
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0answers
90 views
Sticky strike sticky delta implementation
I'm a clear on the differences between the two assumptions but a bit confused on the practical implementation.
1) The aim of choosing one of the two assumptions is to take into account the co-dynamic ...
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1answer
121 views
How do you price an option on multiple things>
Suppose, for simplicity, I want to cover the U.S. stock market by buying ETFs for the Russell 1000 and Russell 2000. But I want to overweight small cap, so the Russell 3000 won't do. Also, let's ...
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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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110 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
157 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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52 views
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?
1
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1answer
96 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 ...
1
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1answer
151 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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56 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 ...
