# Questions tagged [delta-hedging]

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### BSM replication with expiry delta

I’ve been thinking about this problem and I’m missing something. Assuming a BSM world, I sell an OTM option at strike K. I then proceed to delta hedge it at the strike K each time K is touched. Why ...
1 vote
60 views

### How to hedge an options portfolio in hft settings?

Suppose that you are quoting multiple option strikes on multiple levels and getting hit very often. Such trading possesses a challenge from a risk management perspective. To stay delta neutral you ...
• 366
127 views

### Is price really the cost of hedging?

Assume a vanilla option with 1y expiry. The total vol in 1yr is 20 bps, the vol in first 6 months is 5 bps. The price is created by BS(20 bps). But is this price the correct cost of hedging? Will I ...
• 2,451
72 views

### stdev of delta hedged portfolio for call option !=0. Why?

I wrote a Monte-Carlo simulation of delta hedging for a european call. R and Sigma are fixed. I start simulation with zero money and short call option. At each step I borrow money to buy 'delta' of ...
• 166
1 vote
138 views

1 vote
2k views

### Calculating the PnL of a delta-hedged option at a point in time

In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final expected PnL based on implied ...
103 views

### Representing a continuous time hedge discretely

I recently came across an example (Section 5.2.9 here) which does a simple delta hedging experiment. Below are the details: Market conditions Interest rates are at a 2% level --> r = 0.02 The ...
156 views

### How do sell-side institutions manage interest rate derivatives books in practice?

I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such ...
• 814
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### Delta of a forward ATM option

Reading: What are some useful approximations to the Black-Scholes formula? I understand that a ATM Call option can be approximated to $$C(S,t)≈0.4Se^{−r(T−t)}σ \sqrt{T−t}$$ Also, I often hear that an ...
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### pros and cons of hedging oil contracts with options or futures

I work for an oil trading company. We sell petroleum products indexed on the Brent and hedge our fixed price sales using futures to offset price fluctuations. We do not engage in speculation. I was ...
136 views

### How do you explain consistently making money with discrete hedging a call option?

In a backtest I did, I'm selling a call option and buying a delta amount of the underlying (calculated using implied vol). Now I know in the limit case of continuous hedging I end up paying a PnL ...
• 123
1 vote
485 views

### Delta hedging when volatility is stochastic

From my understanding in a BSM world you can make a bet on volatility using options and delta hedging with the underlying. If you think realized volatility of the underlying will be higher than the ...
235 views

### black Scholes model hedging without constant volatility

I have started to look deeply in the hedging and I have created some simulations to simulate delta hedging strategies. I use BS model to calculate delta. The only issue was, which Volatility should I ...
• 154
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### Gamma squeeze - mathematical explanation

I am trying to understand from a mathematical and financial point of view the mechanism behind the so-called gamma squeeze. Is there a good source to read about this/ My questions are: what are the ...
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### Black-Scholes PDE derivation gap

Most derivations of the Black-Scholes formula end up with the following dynamics of some (hedged) portfolio:  \int_{t=0}^{T} \left(\frac{\partial f}{\partial \tau}(S(t),t)+\frac{1}{2}\cdot\frac{\...
87 views

### Option's Delta Investopedia Question

New to this. In this Investopedia article on Delta the following looks like a typo - How Do Options Traders Use Delta? Delta is used by options traders in several ways. First, it tells them their ...
• 101
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### Negative-gamma delta hedging (for a call option writer): how will the stock price affect the portfolio profit?

Suppose a (European) call option writer is hedging their risk by taking a long position in stocks (holding $\delta_C$ shares). The value of the portfolio is $V(S)=\delta_CS-C$. Then is the gamma of ...
1 vote
412 views

### Computing Delta-Hedged Option Returns

I was reading some papers on delta-hedged option returns and came across an intriguing paper that I found quite interesting. However, I was a bit confused on the authors' methodology of computing ...
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### When does the underlying become the derivative?

Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does ...
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228 views

### Option P&L over time

I would like to compute the evolution of the P&L of an FX plain vanilla option. Unfortunately, I am not sure about the correctness of my reasoning. Let's imagine that I sell a 1W call option on a ...
3k views

### How do we hedge option vega practically?

Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
• 196
In Bouzoubaa and Osseiran page 68 equation 5.3, the authors discuss delta hedging a call written for asset $S_1$ using a different but correlated underlying asset $S_2$. The authors provide the ...