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, ...
- 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 ...
- 863
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 $\...
- 8,169
10
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 ...
- 281
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 ...
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 ...
- 5,101
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 ...
- 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 ...
- 6,652
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 ...
- 101
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 ...
- 8,581
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'...
- 8,581
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 ...
- 21.2k
8
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 ...
- 6,084
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 ...
- 12.7k
7
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 $...
- 2,591
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 ...
- 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 ...
- 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 ...
- 6,652
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 ...
- 11.2k
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 ...
- 3,056
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-...
- 4,726
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 $\{...
- 21.2k
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):
$$\forall \, i \in \{1,2\}, dS_i(t) =...
- 8,169
6
votes
Accepted
Principal Components Analysis on overlapping contracts
I would do as follows:
A) First do PCA on an arbitrage-free monthly curve (assuming the most granular contract you will use is individual months). To ensure no arbitrages, you will need to drop out ...
- 1,671
6
votes
How to hedge a perpetual barrier option?
Presumably the option can be exercised for intrinsic at any point. Note the interviewer asked for a static hedge using the stock, not a dynamic hedge. Hence you must find a buy and hold portfolio that ...
- 1,406
6
votes
Accepted
Confusion about replicating a call option
In Black Scholes
$$\frac{dS}{S}=rdt+\sigma dW$$
$dC_{BS}(S,t)=\underbrace{\frac{\partial C_{BS}}{\partial t}dt}_{Theta PnL}+\underbrace{\frac{\partial C_{BS}}{\partial S}dS}_{DeltaPnL}+\underbrace{\...
- 401
6
votes
Accepted
Hedging strategy for payoff $\int_0^T\log S_u\mathrm{d}u$
I assume you want to price a derivative product that pays $\int_0^T\ln S_tdt$ at maturity time $T$, from time $t=0$. I'll ignore generalization to time $t$ because it is trivial (split the integral in ...
- 674
6
votes
What are some interesting recent machine learning related developments in the QF domain?
Empirical Asset Pricing via Machine Learning (2020) by Gu, Kelly and Xiu
- 61
5
votes
why does index futures swing more than index?
The empirical relationship between the futures price $F$ and the spot price $S$ is
$$
F = S e^{b\tau}
$$
where $\tau$ is the time to expiry, and $b$ is the empirical basis, i.e. the number that ...
- 5,931
5
votes
Accepted
How does one calculate the Libor future contract price?
The quoting convention must be explained somewhere in your book.
For Eurodollar futures, this convention is 100 - yield, 92 means the yield is 8% per annum, so for one quarter you need to divide this ...
- 2,908
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