# Questions tagged [black76]

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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 ...
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 ...
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### 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 ...
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 ...
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 ...
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1 vote
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 ...
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1 vote
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 ...
• 111
1 vote
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 ...
• 191
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 ...
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### Black model with negative strike price

Whats the issue if we try to price a swaption with a negative strike using Black model?
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### 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 ...
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:             &...
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### 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 ...
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. ...
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### 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. ...
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### 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%...
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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 ...
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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 ...
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