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Pricing a zero coupon callable bond

Suppose I have a 20-year zero bond with a call date in 10 years and a zero interest rate of 2%, which is currently valued at a Z-spread of 100. Now I would like to evaluate the right of termination ...
Practitioner's user avatar
2 votes
2 answers
876 views

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
1 vote
1 answer
247 views

Question on boundary conditions when using Finite Difference

I have two questions appearing to me (they are not related directly to each other). My first question is about boundary conditions when using Finite difference methods. There are two ways to do it: a)...
alphaH's user avatar
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0 answers
106 views

Black Standard Deviation in QuantLibXL

I was having a doubt about a fucntion in the QuantLib add-on for excel. What is the formula for the function: qlBlackFormulaImpliedStdDev(...) I know that there ...
Tommaso's user avatar
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0 answers
94 views

Can we proof the boundary condition for the Black Scholes derived from a replicating Portfolio?

So for Black Scholes we know that the PDE is the follwing: ${\frac {\partial V}{\partial t}}+{\frac {1}{2}}\sigma ^{2}S^{2}{\frac {\partial ^{2}V}{\partial S^{2}}}=rV-rS{\frac {\partial V}{\partial S}}...
Nikolai Kl's user avatar
1 vote
0 answers
131 views

Why doesn't using the forward as the underlying suffer from pull-to-par and constant volatility in Black's model?

One of the reasons for using Black's model over Black-Scholes to price options on a bond is that the bond price will pull-to-par and hence the constant vol assumption isn't true. Why isn't this also ...
spinthebs's user avatar
2 votes
1 answer
278 views

Black and Scholes pricing

I want to price B&S with $S_t$ stock price that has payoff, $h(S_T)=(S_T^3-S_T^2)^+$. Would it be wrong if I solved as $(S_T^3-S_T^2)^+\implies (S_T^3\geq S_T^2) \implies (S_T\geq 1) \implies (S_T-...
Finance Student's user avatar
1 vote
0 answers
82 views

In building volatility curve for etf options, should I use synthetic forward price or cash price

Assuming option market moves faster than ETF cash price in intraday high frequency setting. That means at each time point, when implied volatility is calculated by black-schole model by using cash ETF ...
tesla1060's user avatar
  • 121
1 vote
1 answer
98 views

Caplet price under stochastic volatility is the black price integrated over volatility distribution

Hull&White 1987 state that when the brownian motion driving the volatility and the brownian motion driving the forward rate are uncorrelated, the caplet price under stochastic volatility is the ...
black88's user avatar
  • 11
0 votes
1 answer
2k views

How to calculate premium in Black Scholes model with quantlib?

I am new to quantlib as well as option price modelling. I need to get premium from black scholes model and found this code in internet ...
Eka's user avatar
  • 647
3 votes
1 answer
576 views

Black's Approximation - Discrete dividend for Put Options

I am currently trying to price and option chain for dividend paying stocks (american style exercise). I am able to calculate the Net Present Value (NPV) of dividends until maturity and then apply ...
peterram's user avatar
  • 103
1 vote
0 answers
7k views

Swaption : Bloomberg Black implied volatility quotes and pricing in the Black model

I used a lot Bloomberg's VCUB for data, but never used its integrated swaption pricer "Quick Pricer for Swaptions", nor Bloomberg's "full" swaption pricer from "SWPM -OV". I am retrospectively quite ...
Olórin's user avatar
  • 1,223
1 vote
1 answer
291 views

Need explanation on weird Gamma Behaviour Black Formula

I am using the RQuantlib package to price options on futures. With a slight modification one can go from the Black Model (76) to The BS Model. It can easily be shown that if we write S0 = (e-rt) * F0 ...
meteoeliot's user avatar
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
0 answers
4k 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 ...
Vladimir Nabokov's user avatar
0 votes
2 answers
2k 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 ...
confused's user avatar
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7 votes
1 answer
963 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 \...
pinaki's user avatar
  • 121
0 votes
0 answers
227 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 ...
dbluesk's user avatar
  • 175
8 votes
4 answers
22k 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 ...
ab94's user avatar
  • 366
3 votes
3 answers
4k 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 ...
Tim's user avatar
  • 163
0 votes
1 answer
200 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
K Smith's user avatar
  • 11
2 votes
0 answers
489 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 ...
athos's user avatar
  • 2,231
4 votes
1 answer
925 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 ...
Lisa Ann's user avatar
  • 2,133
2 votes
1 answer
1k 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 ...
jimifiki's user avatar
  • 235
1 vote
1 answer
241 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 (...
JohnC's user avatar
  • 123
1 vote
1 answer
2k 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:...
Lucas Morin's user avatar
3 votes
1 answer
344 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 ...
user2069136's user avatar