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Delta of Black formula vs numerical

I coded the Black formula (1976) to price a call where the underlying is a forward. I tested it against other sources and it works fine. I then calculated the delta which, from my derivation and what ...
DeltaVanna's user avatar
0 votes
1 answer
253 views

Convergence in the CRR model

Under certain conditions, the option price of the CRR (Cox-Ross-Rubinstein) Binomial model converges to the Black-Scholes price as the maximal step size of the partition converges to zero (i.e. a ...
Kapes Mate's user avatar
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0 answers
259 views

How are SOFR implied vols calculated? Are they normal or log normal?

How are SOFR implied vols calculated? Are they normal or log normal? When we are pricing options with black-76 model, implied volatility must be log-normal as black model assumes log normal ...
Rajat Shubhra Biswas's user avatar
0 votes
0 answers
273 views

Why the sign of RHO in BSM and Black76 Model is opposite?

I find the formula of RHO using Black76 model (Source, alternatively see Wikipedia and scroll to "Under the Black model"): $$ RHO_{call} = -t*c $$ $$RHO_{put} = -t*p$$ which means the sign ...
Hester S's user avatar
2 votes
1 answer
255 views

Interpreting Implied Volatility in Commodities Options

I understand that implied volatility is the expected volatility of an underlying contract in the Black option pricing model. This is easy to interpret for assets delivered at a point in time. But how ...
CasusBelli's user avatar
1 vote
1 answer
258 views

What is the correct volatility to use for inverting Black76?

I'm using VCUB on Bloomberg for ATM cap volatilities and have noticed there are a few "flavors" of volatilities. I would like simply use ATM flat vols to bootstrap forward volatilities from ...
Carp's user avatar
  • 11
1 vote
1 answer
343 views

Black (1976) model growth rate input for futures price

When using the Black 76 model for pricing European index options I've often seen people use 2 different rates: the typical risk free rate used to get the discount factor, and a growth rate used to get ...
Kevin K.'s user avatar
  • 111
1 vote
3 answers
558 views

options on futures

For options on futures in the black model, I do remember that $F$ appearing in the formula must be the forward at maturity of the option (and not the future price). So, say we have a future maturing ...
volatile's user avatar
  • 191
2 votes
1 answer
509 views

Black76: Pricing options on futures

I am trying to roughly approximate (not really price) options on VIX futures whereby the VIX future is estimated using their bounds. If the option is approximated using the Black model, how do you ...
deblue's user avatar
  • 281
0 votes
0 answers
95 views

Black model with negative strike price

Whats the issue if we try to price a swaption with a negative strike using Black model?
Rejath Johny's user avatar
0 votes
0 answers
230 views

Bond Options Calibration to market volatility using SABR Model

I'm trying to calibrate bond option implied volatility from SABR model to market volatilities, I tried calibration in python but the smile isn't correctly matching with market volatility? Any help is ...
Ashwin Mvs's user avatar
2 votes
0 answers
353 views

SDE of futures price under non-constant interest rate and volatility process

I'm trying to figure out the form of the SDE of futures price under the risk neutral measure, when stock price follows GBM:             &...
Yilie Ma's user avatar
  • 105
4 votes
2 answers
3k views

1y10y vs. 10y1y Swaption

Say you have two identical payer swaptions, exception for their terms and tenors. In other words, suppose you have two payer swaptions: $1y10y$ and $10y1y$. All other things being equal, according ...
Vladimir Nabokov's user avatar
3 votes
1 answer
2k views

Obtaining swaption prices from lognormal volatility quotes

I am working with the following dataset from quandl: https://www.quandl.com/databases/CSWO (I'm using the sample dataset only). My question is how to obtain the swaption prices from the quotes given. ...
lbf_1994's user avatar
  • 383
0 votes
1 answer
284 views

Black 1976 caplet value

I've seen from two sources different formulas for the caplet value (Black 1976): $$Caplet_1 = N\cdot DiscountFactor_{0,k}\cdot yrFrcn_{k,k+1}\cdot [F_{k,k+1}\cdot N(d_1) - R_k\cdot N(d_2)]$$ $$ ...
Oliver Mohr Bonometti's user avatar
7 votes
1 answer
2k views

Black-Scholes vs Black equation

Why is Black used for interest rate options pricing instead of Black-Scholes? Why are we more interested in Future rates instead of Spot rates when it comes to interest rate options? Basically, why ...
Filip Bašić's user avatar
1 vote
2 answers
478 views

Use of Historical Volatility in Black 76 Model

I am trying to use the Black 76 model to calculate the price of a bond option. Is it possible to use the historical volatility of the bond prices (say standard deviation of the log returns over the ...
user30865's user avatar
3 votes
1 answer
492 views

Pricing and Hedging an Option through a Currency Triangle

How is the option price of an plain vanilla option (in a Black Scholes setting) derived, which is written on, say XAGGBP but practically hedged with XAGUSD and GBPUSD (because these are more liquid)? ...
Tim's user avatar
  • 163
3 votes
2 answers
595 views

FX Option Pricing Under Basis Adjustment

Given money market rates such as USD LIBOR and EURIBOR and in the context of FX options valuation, I have been reading about the importance to include a so called basis adjustment to one of the ...
Tim's user avatar
  • 163
0 votes
1 answer
776 views

Black's model and Monte Carlo

It is well know that one uses the Black 76 model to price commodity derivatives. I would however like to perform a Monte Carlo simulation that ties back to this number. How would one go about this ...
User16473932's user avatar
4 votes
2 answers
3k views

Which models do Bloomberg/Reuters use to derive implied volatility for interest rate derivatives with negative forward rates?

can anybody tell me which models Bloomberg and Reuters ares using to derive implied volatility for interest derivatives with negative forward rates? I know that Black-76 is the standard model, and ...
Philipp's user avatar
  • 41
1 vote
1 answer
144 views

Relation between Libor market model and Black76 with time-dependent vola

The Black76 model uses a lognormal process to model the forward rate $L_1(t)$ from $T_1$ to $T_2$ at time $t$, $$dL_1(t) \ = \ \mu(t) L_1(t) dt + \sigma(t) L_1(t) dW_t$$ By switching to the $T_2$-...
davidhigh's user avatar
  • 348
1 vote
1 answer
3k views

Why is the Black 76 model not considered an interest rate model?

The Black 76 model is one of the standard models for interest rate derivatives like pricing caps, floors, swaptions, etc. The Black 76 model is given as $$dF_t = \sigma F_t dW_t$$ so it models the ...
dnl's user avatar
  • 410
0 votes
1 answer
160 views

Premium result with BlackProcess not in line with online engines

I'm trying to implement BlackProcess with Quantlib (in C#) and the result I get for NPV() is not inline with some resources I can find online. Here is my code: ...
Askolein's user avatar
  • 103
3 votes
1 answer
268 views

Why is there an upper limit on the premium of an ATM (!) call swaption in the Black76 model?

Trying to imply Black76 (where the forward swap rate is log-normal) volatilities as Bloomberg does in their VCUB screen we see holes at two regions: at short maturities due to negative rates which ...
Richi Wa's user avatar
  • 13.8k
3 votes
1 answer
1k views

Valuation of option on amortized IR swap

I'm currently valuing swaptions using an implied volatility surface and Black's formula. This formula is given by $$A (S\Phi(d_+) - K \Phi(d_-))$$ where $$ d_{\pm} = \frac{\log\left(S/K\right) \pm \...
Olaf's user avatar
  • 1,909
8 votes
3 answers
21k views

How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?

In markets, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? Is it normal volatility, or lognormal volatility. because it affect our hedging positions. ...
Amiro's user avatar
  • 340
2 votes
1 answer
80 views

Likelihood of a caplet ending in the money

with what likelihood would one expect an ATM caplet to end up in the money? Just as a very rough guess, from real world experience. When I consider N(d2) from the Black formula, for spot = strike = 4%...
ettlich's user avatar
  • 21
6 votes
2 answers
2k views

good R package for vectorized option pricing

I am using for now the package fOptions but it doesn't allow for vectorized computation of black76 prices and delta. Which package can be used to do that? As noted ...
RockScience's user avatar
  • 2,003
6 votes
1 answer
245 views

BlackProcess' constructor $x_{0}$ argument in QuantLib

I am currently using BlackProcess to price options and I have a doubt related to the $x_{0}$ argument of the constructor: I've figured out it should be the forward ...
Lisa Ann's user avatar
  • 2,133
3 votes
1 answer
2k views

What is the Rho of an option on a futures contract priced using the Black 76 model?

I wanted to quickly confirm some simple calculations for the Black 76 greeks and was making use of the formulas on this website: http://riskencyclopedia.com/articles/black_1976/ I have an issue with ...
Ben's user avatar
  • 143