Questions tagged [delta-hedging]

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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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74 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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109 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+\...
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2answers
76 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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154 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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91 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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37 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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88 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 ...
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1answer
97 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 ...
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176 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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36 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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70 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 ...
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66 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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55 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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133 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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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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35 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 ...
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1answer
151 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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131 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 $<...
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97 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 ...
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1answer
109 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 ...
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1answer
91 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 ...
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1answer
295 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 ...
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1answer
70 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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53 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-...
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2answers
364 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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96 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 ...
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1answer
214 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
258 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
108 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 ...
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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 $...
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145 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 ...
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151 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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104 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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83 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
117 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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39 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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100 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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145 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?
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94 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
136 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 ...
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155 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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818 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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166 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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212 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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119 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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396 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 ...