Skip to main content
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, ...
Peter A's user avatar
  • 494
13 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 ...
SI7's user avatar
  • 843
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 $\...
Daneel Olivaw's user avatar
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 ...
RWP - Down by the Bay's user avatar
10 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 ...
demully's user avatar
  • 5,071
9 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 ...
phlsmk's user avatar
  • 725
9 votes
Accepted

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 ...
AlRacoon's user avatar
  • 6,612
9 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 ...
OGC's user avatar
  • 271
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 ...
HowtoETF101's user avatar
9 votes
Accepted

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 ...
Bob Jansen's user avatar
  • 8,562
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'...
Bob Jansen's user avatar
  • 8,562
8 votes
Accepted

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 ...
Gordon's user avatar
  • 21.1k
8 votes

Pricing and hedging caps and floors on illiquid emerging markets

It could be worse. You're not asked to price rate exotics like accreters that might need more inputs besides implied vol cube :) and you're only asked to make markets. I.e., if I understand the ...
Dimitri Vulis's user avatar
7 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 ...
LocalVolatility's user avatar
7 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 ...
Bram's user avatar
  • 812
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 ...
siou0107's user avatar
  • 2,680
7 votes
Accepted

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 ...
AlRacoon's user avatar
  • 6,612
7 votes
Accepted

Hedging a trade for PCA component neutrality

Simple Directionality Spread Trade Hedge If the sum of the risks of the trade $t$ are zero (as in the case of the 2Y5Y10Y spread trade) that immediately gives a starting point from which to make a ...
Attack68's user avatar
  • 10.5k
7 votes
Accepted

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 ...
StackG's user avatar
  • 3,026
7 votes

What are some interesting recent machine learning related developments in the QF domain?

Sirignano, J., & Cont, R. (2019) (High-frequency stock forecasting): The authors apply a large-scale deep learning model (recurrent neural network with Long Short-term Memory units) to high-...
Pleb's user avatar
  • 4,286
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
eltigrechino's user avatar
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 $\{...
Gordon's user avatar
  • 21.1k
6 votes
Accepted

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) =...
Daneel Olivaw's user avatar
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 $...
will's user avatar
  • 2,571
6 votes
Accepted

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 ...
ZRH's user avatar
  • 1,671
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 ...
Ivan's user avatar
  • 1,396
6 votes
Accepted

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{\...
ryc's user avatar
  • 401
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 ...
Soumirai's user avatar
  • 624
6 votes

What are some interesting recent machine learning related developments in the QF domain?

Empirical Asset Pricing via Machine Learning (2020) by Gu, Kelly and Xiu
TwoII's user avatar
  • 61
5 votes

why does index futures swing more than index?

The empirical relationship between the futures price $F$ and the spot price $S$ is $$ F = S e^{b\tau} $$ where $\tau$ is the time to expiry, and $b$ is the empirical basis, i.e. the number that ...
Chris Taylor's user avatar
  • 5,931

Only top scored, non community-wiki answers of a minimum length are eligible