Financial Engineering Course: Lecture 7/14, part 1/2, (Swaptions and Negative Interest Rates)

[@sungchulyonseiackr]

Great lecture, Lech! @9:44 Black's formula in ppt seems not correct. 1 First of all the libor rate fluctuates in [t_0,T_{k-1}], not [t_0,T_k]. So, in the definition of d_1 and d_2 I think T_k-t_0 terms are typos and should be T_{k-1}-t_0. I could not find this formula in your great book, but found it in page 439 of Shreve's Stochastic Calculus for Finance II. I would like to check whether my understanding is correct. Thanks, in advance. 2 In line -3 N_k ---> N, K_k ---> K

[@ComputationsInFinance]

hello Sungchul Lee, you are perfectly correct, I have just corrected the slides and uploaded on GitHub. Thanks a lot for the notification. Best wishes, Lech

[@goldenham89]

@43:00 Hello professor, I think that w_k(t0) = tau_k * P(t0, Tk) / Am,n(t0) is correct instead of w_k(t0) = tau_k * P(t0, Tk) * Am,n(t0). How do you find it?

[@ComputationsInFinance]

hello Jaeyong, thanks for your feedback! Indeed you are right, it should be divided, and not multiplied. I will fix the slides! Thanks again. Best wishes, Lech

[@honcheunghui5684]

Could you explain the cash and physically settled swaption?

[@ComputationsInFinance]

Sure, in short: at the expiry, in the physically settled swaption you will enter a swap, and in the cash settled swaption, you will receive cash, based on a formula. Keep in mind that cash settled swaptions based on formulas are outdated and not so common any more (because of the formula which is very heuristic). I hope it explains. Best wishes, Lech

[@minhle9868]

Great lecture thanks Lech! Just a quick question regarding the industry practice, is Hull-White the most popular model being used out there based on your experience? Think I need to sit down and do more exercises on it.

[@ComputationsInFinance]

hello Minh, indeed, the HW model is the most popular however it is not the best. There are models that are significantly better in terms of calibration to swaptions and more exotic derivatives, however these models typically lack the simplicity that the HW model has. Cheers, Lech

[@armandcharlesngabirano3795]

Excellent sir..however I have one question how do we get to find lamda and eta values for the hull and white model?

[@ComputationsInFinance]

hello, thanks for the feedback. To get mean-reversion and the volatility parameters for the Hull-White model you need to perform model calibration. There are many different ways to calibrate the HW model, one possibility is to calibrate it to swaptions. Everything depends on the purpose, i.e. what are you planning to use the model for? Hope it clarifies, Best, Lech

[@armandcharlesngabirano3795]

Dear sir I come here again with a small question...the lines 146 and 167 for the strike price K= np.linspce (- shift, np.abs (L0) for the shifted log normal model why do you multiply By 3.25 and 6.0,25?

[@ComputationsInFinance]

hello Armand, yes, indeed, these are not consistent. In one case I wanted to show implied volatilities and in the other one I was illustrating prices. The practical problem with implied volatility for large strike is that your Newton-Raphson formula may fail (This is why you prefer that range to be narrower). Otherwise, there is no other reason. I hope it explains. Best, Lech