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Questions tagged [black]

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0
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0answers
28 views

Black Litterman - Sector rotation

I was wondering if anyone here have ever tried to introduce sector rotation with regards to the Black-Litterman model. I want to try to expand the BL model by introducing this feature, however I have ...
2
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1answer
267 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 ...
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0answers
539 views

Black-76 Model for Swaption Price and Greeks

I'm in the early stages of developing a swaption pricing model. Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
0
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2answers
347 views

Is the delta of a binary option the same as the delta for a regular European option?

Assume both options have strike of 100, same time to expo, no dividend, same interest rate, same vol and lets say underlying is trading 95. Do both have the same deltas? I read this and still don't ...
6
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1answer
364 views

Black Derman Toy model: from tree to differential equation

The Black Derman Toy model of interest rates is usually introduced as the model governed by the stochastic differential equation: $$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
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0answers
107 views

Black's formula for a call option on a non-tradable underlying

I am looking for an explanation of the following fact, which seems to be rather simple yet I am missing something. Say that $S_t$ is a stock following GBM $$ dS_t = r S_td_t + \sigma S_t dW_t,$$ and ...
3
votes
4answers
4k views

Which risk-free interest rate to use in Black-Scholes equation

Sorry but i'm new in quantitative finance. According to BS derivation the risk-free interest rate is the rate to wich the rate of a particular investment tends when the risk tends to zero. Suppose i ...
0
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2answers
777 views

FX Option pricing on Forward vs. Spot

In a GBM world with riskless domestic and foreign interest rates, what would be the correct model for a FX plain vanilla option given the statement that this option is priced on the forward? I guess ...
0
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1answer
92 views

Why is the forward rate used for the underlying in Black's model?

Why is the forward rate suitable for being used as the underlying in Black's model? Thanks
2
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0answers
353 views

How to calibrate volatility surface for Interest Rate Cap&Floor pricing

I'm using Black model to do interest rate Cap & Floor pricing. The volatility is determined by using the bootstrapping methodology. However, afterwards, how should I do the calibration, or ...
4
votes
1answer
430 views

Black model: Delta - strike relationship regardless of expiry?

While wandering through some QuantLib experimental classes for FX trading, I've found this Black Delta Calculator. By reading its .cpp, it seems that no use of ...
2
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1answer
803 views

How does Reuters quote caps?

I'm wondering which curves should I use when passing from the Implied volatility to prices. When I read an implied volatility (for instance 3Y Cap strike 0.5%) the discounts and forward rate ...
1
vote
1answer
185 views

In a Black-Scholes world, why must volatility be strictly increasing in time-to-expiration?

This question is from Rebonato's Volatility and Correlation 2nd Edition. Rebonato states that if $\sigma_T^2T$ is not strictly increasing, it would be simple to set up an arbitrage. Unfortunately (...
1
vote
1answer
1k views

Interpolation of volatility curve for Swaption

I have found volatility in the black model for swaption for different maturity (1-2-3-6-9M, 1Y, 18M, 2-10Y, 15-20-25-30Y) and Tenor (1-10Y, 15-20-25-30Y). Now I need another values (Maturity: 2, Tenor:...
3
votes
1answer
215 views

Pricing of a simple contingent claim

Earlier I had the question (5.11 Tomas Bjork): $$ \frac{\partial F}{\partial t}+\frac{1}{2}x^2\frac{\partial^2 F}{\partial t^2}+x = 0 $$ $$ F(T,x) = ln(x^2) $$ And solve it using Feynman-Kac. The ...