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36 votes
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Have Goldman Sachs Quantitative Strategies Research Notes been published as a book or a comprehensive collection?

Many of them are on my website at emanuelderman.com. Others I probably have anyway. Feel free to email me
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16 votes

Mark Joshi's book - quant interview questions

For large values of the spot S, this payout goes to infinity like the square of S. However, the hedging instruments available are vanilla options, which go like S to the first power. Mathematically, ...
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  • 456
14 votes

How to gamma hedge and vega hedge an autocallable product?

Well, it's a topic which actually should have its own book dedicated. Unfortunately, existing literature is rare or not practical enough. Let me at least try to provide some key ideas and challenges ...
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  • 721
12 votes

Mark Joshi's book - quant interview questions

I suspect this is because, conditional on being in-the-money, the payoff of your option is convex in stock price $-$ whereas for a vanilla call, the payoff is linear. As a consequence, the delta $\...
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11 votes

Have Goldman Sachs Quantitative Strategies Research Notes been published as a book or a comprehensive collection?

I had read some of them; actually, it does not exist an on-line library that collected them (or, better, it existed here, but it seems the website does not work anymore). I reported here below some ...
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  • 2,438
10 votes

Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?

the problem is that the pay-off has discontinuous first derivative. Try a contract with pay-off that is twice differentiable and it will probably work. The problem is that all the value comes from ...
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  • 6,743
10 votes

Hedging Covid-19 and other low probability high loss risks

There's no easy answer to your question, as noob2 pointed out. You can look online for info from Universa. That fund does exactly what you are asking: https://www.universa.net/riskmitigation.html ...
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9 votes

When should we delta hedge?

By delta hedging you are saying that you have a view on the path and the volatility of the option you are trading, but not on its direction; in your case, that being short delta. From a theoretical ...
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9 votes
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How do traders hedge against “tail side risk” in practice?

With difficulty and high costs and secretively. Successful ones are the ones that are able to do it more cheaply. This is also the reason for their secretiveness: prices would go up. The costly but ...
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  • 7,652
9 votes

Who hedges (more): options seller or options buyer?

Your question comes at this correctly, in my opinion. There is indeed a buyer and a seller behind every option; but the hedging behaviour of the two need not be equivalent... I used to work in an ...
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  • 4,896
8 votes
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Why is $N(d_2)$ not needed for hedging?

The point is the following: Delta, $\Delta$, is defined as $\frac{\partial C}{\partial S}$, where $C$ is the value of the call option, and $S$ is the price of the underlying asset. So, given that ...
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8 votes

Creating a Beta-Neutral Portfolio

There are more ways to approach this but the method I propose should work reasonably well in practice, especially if you increase the number of assets you hold. Calculate the beta of the stocks you'...
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  • 7,652
8 votes
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Dynamic Hedge of Quanto Options

Your simulation is basically fine, though you need to discount in USD. For hedging purpose, you need to use the instruments available in USD. Let $S=\{S_t, \, t\ge 0\}$ be the stock price process in ...
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  • 20.4k
8 votes

Delta hedging on Barrier/Digital Options

You're right that the "real" greeks of a digital option are unwieldy, e.g. delta is zero everywhere except at the barrier where it is an impulse. So sell-side trading desks model/price digital options ...
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  • 705
8 votes
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What really is Gamma scalping?

Assuming all else remains equal (implied vol has not changed and very little time decay has occurred), Gamma scalping can best be explained by Gamma (or realized volatility) enhancing the value of a ...
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  • 5,255
7 votes
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derivation of the hedging error in a black scholes setup

The differential equation has a trend due to the interest rate. When you discount you take this trend away: $$ \frac{d}{dt} (e^{-rt}Z_t) = -re^{-rt}Z_t + e^{-rt} \frac{d}{dt}Z_t = e^{-rt}\frac{1}{2}...
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  • 3,826
7 votes

What really is Gamma scalping?

Gamma scalping (being long gamma and re-hedging your delta) is inherently profitable because you make 0.5 x Gamma x Move^2 across the move from your option. (You get shorter delta on downmoves, so you ...
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  • 221
7 votes

How to adjust delta hedging if stock price decreases?

You are long a vanilla option, so long gamma (positive gamma). If the stock price decreases, so does the delta of your option. Since you short-sold the stock to hedge, you now have short-sold too ...
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  • 2,350
7 votes
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How to adjust delta hedging if stock price decreases?

You would be over hedged in your call position if it was delta neutral before the stock cratered. Since you are long delta on the call, you would have shorted stock to make the original position ...
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  • 5,255
7 votes
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Static vs Dynamic Hedging: when is each one used?

It depends a little bit what you're trying to do. If you can statically replicate the payoff of a position at $t=0$, then putting on that hedge will insulate you from all risk coming from the ...
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  • 2,836
6 votes

How do market makers hedge VIX index options?

Due to the lack of a carry arbitrage, VIX futures are actually the direct hedge for VIX Index options
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6 votes

Ito lemma of Convertible Bond under Two-factor Model Interest Rate

Let $V(t, r_t, S_t)$ be the convertible bond price at time $t$, where \begin{align*} dS_t &= S_t(r_t dt + \sigma dW_t^1)\\ dr_t &=\kappa(\theta-r_t)dt+\Sigma dW_t^2, \end{align*} and where $\{...
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  • 20.4k
6 votes

Continuous delta hedge formula

This is a slightly extended version of my comment that summarizes the main result of the reference that I provided. This problem is discussed in detail in Chapter 12 of Wilmott (2006), which is based ...
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6 votes
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Replicating a portfolio with a certain payoff function

A general hedging strategy Let assume that $S_1(t)$ and $S_2(t)$ are the price processes of your 2 stocks and that they follow a Geometric Brownian Motion (GBM): $$\forall \, i \in \{1,2\}, dS_i(t) =...
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6 votes

Delta hedging on Barrier/Digital Options

I nearly agree with @phlsmk's answer, but with some small differences. First off, the delta of a digital is not "zero everywhere except at the barrier where it is an impulse". This is what it is at $...
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  • 2,406
6 votes

What really is Gamma scalping?

As long as you live in a world where implied and realized vol are the same, there is no net profit (or loss) from gamma scalping. However, if they are different, then you make a gain or loss which is ...
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  • 794
6 votes
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Principal Components Analysis on overlapping contracts

I would do as follows: A) First do PCA on an arbitrage-free monthly curve (assuming the most granular contract you will use is individual months). To ensure no arbitrages, you will need to drop out ...
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  • 1,581
6 votes

How to hedge a perpetual barrier option?

Presumably the option can be exercised for intrinsic at any point. Note the interviewer asked for a static hedge using the stock, not a dynamic hedge. Hence you must find a buy and hold portfolio that ...
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  • 1,356
6 votes
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Confusion about replicating a call option

In Black Scholes $$\frac{dS}{S}=rdt+\sigma dW$$ $dC_{BS}(S,t)=\underbrace{\frac{\partial C_{BS}}{\partial t}dt}_{Theta PnL}+\underbrace{\frac{\partial C_{BS}}{\partial S}dS}_{DeltaPnL}+\underbrace{\...
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  • 356
6 votes
Accepted

Hedging strategy for payoff $\int_0^T\log S_u\mathrm{d}u$

I assume you want to price a derivative product that pays $\int_0^T\ln S_tdt$ at maturity time $T$, from time $t=0$. I'll ignore generalization to time $t$ because it is trivial (split the integral in ...
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