6 votes

Delta of Black formula vs numerical

Your Delta_fd is forward delta (you're bumping the fwd). Delta is spot delta. Hence the discount factor.
user35980's user avatar
  • 1,386
6 votes
Accepted

Attributing change in option prices to greek components

Suppose that the fair value of your option is a function $f$ of 3 inputs: the price of the underlying, the implied volaility, and time. You want to understand why the function value changed from time $...
Dimitri Vulis's user avatar
5 votes
Accepted

The derivation of vega/gamma relationship

Just want to add the observation that the pricing PDE solution can be formally written as $$ C(\tau) = e^{\tau \mathcal H} C(0) \quad (*) $$ where $\tau$ is time to maturity and $\mathcal H$ is a ...
Frido's user avatar
  • 1,854
4 votes
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QuantLib: Analytical Greeks and Numerical Greeks do not match?

How close the numerical Greeks are to the analytic Greeks depends on how one calculates them. The analytic Greeks correspond to the mathematical derivatives, so in general smaller increments should ...
Luigi Ballabio's user avatar
4 votes

Selling Strangle or Selling Straddle

There's a reason why the otm IVs are higher to begin with. Market moves/returns exhibit kurtosis. This implies most of the time they move in a confined range, from time to time they exhibit very large ...
user68819's user avatar
  • 395
4 votes

Selling Strangle or Selling Straddle

This is a bit like saying it's "a superior strategy" to lend $100 for 2 years rather than for 1y year because you earn twice as much interest. The skew premium is there to reflect ...
user35980's user avatar
  • 1,386
4 votes
Accepted

Delta of Black formula vs numerical

I think I disagree here. FD delta should yield a value that is very close to $exp^{-rT} * N(d1).$ If not, I think you may use a non-conventional implementation of Black-76. Also, you wrote that your ...
AKdemy's user avatar
  • 8,739
4 votes

What is the P&L

Can’t be calculated precisely from the information given, but we can make an approximation: -first, assume that you delta hedged your call so we start with a delta neutral portfolio -second, note that ...
dm63's user avatar
  • 17.1k
3 votes

Why are Black-Scholes derived greeks used for risk management when alternatives exist?

I do not agree with the answer by @river_rat. SABR greeks (the so-called Bartlett delta and vega) are used by practitioners in Interest Rates trading from my own experience. In general you want your ...
Hasek's user avatar
  • 814
3 votes

From parameter risk (sensitivities) to market risk (sensitivities)

Formally, you have two ingredients: a pricing function for your specific instrument, $f$, that depends on some set of model parameters $\mathbf{r}$ a parameterization $\mathbf{F}$ that consistently ...
Kermittfrog's user avatar
  • 6,618
3 votes

0DTE volatility and greeks

You don't. The problem is that when the time horizon is so small, if the options isn't perfectly ATM, the gamma and vega $\approx0$, and delta $\approx1$. A small shift in the underlying further OTM/...
THAT'S MY QUANT MY QUANTITATIV's user avatar
3 votes

Option Greeks' Formulas for Black & Scholes vs Black 76

Black-Scholes model is used to price options on spot while Black76 is used for pricing options on futures contracts. For European options both models will give exactly same price given options expiry ...
user2329744's user avatar
2 votes

The derivation of vega/gamma relationship

Even though it is true that the volatility is constant in this setting, the relationship is valid for all terminal condition or pay-off function -- beyond the typical $(\pm(S-K))_+$ -- so long as the ...
Hans's user avatar
  • 2,806
2 votes

Calculating the Delta of FX option

What you look at here is not a normal option. The type is called DIVA, which stands for digital vanilla, which is a binary option. Bloomberg computes this via a tight spread. However, you have a few ...
AKdemy's user avatar
  • 8,739
2 votes
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Why do the Greeks not converge to the strike as the volatility tends to zero?

If you shrink the volatility (let's say more extreme it goes to zero), then the spot price at maturity is simply $S_t e^{r(T-t)}$. There are no uncertainty; the at-maturity spot price becomes somehow ...
JamesWuuuu's user avatar
1 vote

Why are Black-Scholes derived greeks used for risk management when alternatives exist?

Pick your poison, what is better? A simple model that is wrong or a complicated model that is also wrong. Add to that computation time on large portfolios and the simplicity of a closed form Black-...
river_rat's user avatar
  • 980
1 vote

Moneyness, implied volatility and option greeks

For the first question: The differences in IV across strikes is largely due to the market having a different view on potential movements than a constant-volatility model (like Black-Scholes) would ...
D Stanley's user avatar
  • 1,356
1 vote

What does it mean with regards to market conditions that the historical volatility is twice the implied volatility

Factually, it means that traders are pricing options as if they were less volatile than what actually happened in the past. It's easy to conclude that this means people generally believe the ...
gomennathan's user avatar
1 vote
Accepted

Theta using black scholes when time to maturity approaches 0

It is true that it is common that BS theta exceeds the actual market value of an option if the time to expiry is short. Therefore most systems compute theta via finite difference (FD) as a true 1 day ...
AKdemy's user avatar
  • 8,739
1 vote
Accepted

Beta adjusting change in market value

There is no intuitive answer, since beta is about covariance of returns with the market and not necessarily about market cap changes. Now if you think carefully, a company with a persistent $\beta$ ...
phdstudent's user avatar
  • 8,306
1 vote

Link between Vega and Gamma

I believe in its most fundamental form it is best to internalize that the expected gamma rebalancing P/L = Option price at one volatility. Thus the difference of the option prices at different ...
XXXXXXX's user avatar
1 vote

What is gamma to do with realized volatility?

Gamma tells you how much your delta changes as the underlying price moves back and forth. If the gamma is positive it means that the delta increases as the underlying goes up, and delta decreases as ...
Newquant's user avatar
  • 769
1 vote

How do we hedge option vega practically?

Just adding my 2 cents. The skill of the role is to collect bid offer on average. Therefore, there will most definitely be times where your positions carry you out and you are forced to lose some or ...
user68819's user avatar
  • 395
1 vote

Problem with the concept of Dollar Gamma

From the second order Taylor expansion (variational principle) of a value of an option V around the underlying S, we have: $$ \Delta V = { \partial V \over \partial S } \Delta S + { 1 \over 2 } { \...
Dorian B.'s user avatar
  • 121

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