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6
votes
0answers
166 views

American Swaption Heding with Malliavin Calculus

Hedging American Swaption Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t. $$ C_t = (\delta \sum_{j=n+1}^{M+1} ...
4
votes
1answer
309 views

Is Cubic spline Interpolation on swaption Volatility arbitrage free?

If I use interpolation technique such as cubic spline to estimate volatility of Swaption with different strike,(with a given forward rate, swap and option maturity) will this be arbitrage free? What ...
4
votes
1answer
362 views

Greeks of a swaption using Brigo

I struggeling with calculating the delta of a swaption. In the interest rate case I usually mess around with the multiple cash flows over time so that the discounting is more complex than in the ...
4
votes
2answers
206 views

Machine learning for non optimal behaviour

I was working on the pricing of complex bermudean swaption when I noticed that the exercise is often (very) subobptimal. It seems that the clients are more sensitive to past growth or drop in rates ...
4
votes
1answer
74 views

Swaption Volatility Cube arbitrage

How can I exploit an arbitrage by violating the following no-arbitrage condition (taken from the paper "Arbitrage-Free Construction of the Swaption Cube" by Simon Johnson and Bereshad Nonas): ...
4
votes
1answer
111 views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
3
votes
1answer
60 views

Why can a swap option be regarded as a type of Bond option?

Why can a swap option be regarded as a type of bond option? My idea: Suppose the swap rate of the swaption is $s$. Now consider a bond option expiring at $T$ with strike, $(P_K)_t = ...
3
votes
1answer
48 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 ...
3
votes
1answer
45 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 ...
2
votes
2answers
72 views

Is there any template of hull white one-factor calibration model?

Recently I would like to look for excel template of hull white one-factor calibration model using swaption data for my urgent task? However, it seems that I cannot find suitable one in the web. ...
2
votes
1answer
239 views

Swaptions vol trading lognormally

What does this mean: "Front-end vols have been trading lognormally while longer tails have traded normally." I read this in a research report, in the context of ...
2
votes
1answer
582 views

European Swaptions: does implied volatility of swap rates decreases both with start and tenor?

Does implied volatility of swap rates decreases both with start and tenor? Given a Swaption price and a discount curve I calculate the swap_rate from the curve, then I define implied volatility as ...
2
votes
2answers
229 views

swaption model for forward swap rate

I have another question about interest rates. In this case it is about swaption and how to come up with a pricing formula. For the rest of my question I use the notation from Brigo. The payoff of a ...
2
votes
1answer
203 views

LMM. Calibration to swaptions by Brigo and Morini. Volatility of swaption that matures at T=0

I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini. I ...
2
votes
1answer
452 views

American Swaption Pricing with Monte-Carlo method

I want to price an American swaption but I am not sure about what I am doing. Tree methods and PDE discretization seem difficult to adapt to a swaption. I am trying a Monte-Carlo approach. (in ...
2
votes
0answers
164 views

Weighted average implied optionlet/swaptions volatility

Let an implied volatility curve/surface is made up by optionlets or swaptions Black's implied volatility. If you wanted to price, say, a FRN with cap and/or floor, a CMS et cetera you would input the ...
1
vote
2answers
76 views

Is “Issuer and Holder with same strike” meaningless?

I've seen a callable putable bond whose first exercise date is an exercise date both for the holder and the issuer. Moreover both strikes have the same value: 100. I wonder what does it mean. I ...
1
vote
1answer
93 views

Determining swaption prices using the characteristic function

There exist multiple techniques to determine call option prices that make use of the characteristic function. These techniques boil down to some integral expression of the option price in terms of the ...
1
vote
1answer
349 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, ...
1
vote
1answer
439 views

How to calibrate the Hull-White model using cap prices?

I'm given cap prices and swap rates, and i'm trying to calibrate the Hull-White model to them. I then want to use the model in order to price a swaption. I know that the model can be calibrated from ...
1
vote
0answers
65 views

Price 3m libor autocap with LMM calibrated on 1y swaption data

I need to calculate a price of an autocap contract which is An autocap is similar to a cap, but at most γ ≤ β caplets can be exercised, and they have to be automatically exercised when in the ...
1
vote
0answers
137 views

American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
1
vote
0answers
109 views

Recalibrating SABR parameters for Swaption ATM volatility

I understand that the ATM volatility of Swaption moves quite frequently and the SABR will need to be recalibrated. Which parameter should I recalibrate? Is there any financial meanings why we only ...
0
votes
1answer
40 views

Swaption on a swap with 0 year tenor

Any ideas on valuation of IRS swaption on a swap with 0 year tenor? As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...
0
votes
1answer
28 views

SABR Calibration: Normal vs Log-Normal Market Data

This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions. So let us define ...
0
votes
0answers
12 views

Accuracy Rebonato Swaption Approximation Formula among Different Strikes

Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes? My foundings: Let $0 ...
0
votes
0answers
41 views

Normal Black&Schole model for swaptions isn't working properly

I just wrote two functions in Matlab which calculates the swaption prices based on the Lognormal model and on the Normal model, although I have the idea that the Normal model is wrong because the ...
0
votes
0answers
60 views

BDT model calibration using swaptions

I am using the Black-Derman-Toy model in a binomial tree that lasts 5 years with time increments of 1/12 . I have to calibrate my model using swaptions but I don't know which maturity I should use. I ...
0
votes
0answers
276 views

Calibration Problem in the LMM-Skew (Shifted Diffusion) Model

I have implemented the LIBOR market model (LMM) and I am quite satisfied with the results. I have now added a skew to the model as described in 10.1 of Brigo/Mercurio. That is, I have replaced the SDE ...