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2d
answered KeyError in Python code used to determine a trade signal for Pair Trading
Apr
11
answered Compute the (Net) Present Value
Apr
11
revised Determining swaption prices using the characteristic function
edited title
Apr
11
asked Determining swaption prices using the characteristic function
Apr
11
answered Identity given in Shreve volume 1
Apr
3
comment Euler discretization of Heston SDE in Mathematica
Another thing you could check is the distribution of the end-points of the generated Paths (e.g. a histogram). This should resemble something log-normal like, but with fatter tails.
Apr
3
comment Euler discretization of Heston SDE in Mathematica
Tricky to debug, because I dont have Mathematica. Is writing T as a fractional a potential cause for slowing down your code? I know mathematica likes to keep fractional expressions for as long as possible. 1 hour is quite excessive. Also, shouldn't the Dividend be set to zero in BCallIV?
Mar
30
comment Java Implied Volatility Solving with Newtons Method
@Hans: are you saying that, in all circumstances, any (positive) initial volatility will converge to the correct implied volatility? Because my point is that this is not the case... And yes, the numerical instability comes from floating point precision error. I burned myself a few times on that with Newton's method.. but maybe not in the context of implied volatility.
Mar
28
comment Java Implied Volatility Solving with Newtons Method
If your initial guess is too poor then it is also possible for Newton to "overshoot" after a few iterations and land on a negative volatility. This is a big downside of Newton's method, in addition to its numerical instability in regions where Vega is practically zero. The pricer and Greeks are not defined in the domain of negative vol, so they could generate all sorts of nonsense. Bisection is slower, but more stable since the algo stays within the initial bounds set by the user, so that is probably a good way to go.
Mar
28
answered Implied Vol vs. Calibrated Vol
Mar
24
comment Why the Black-Scholes formula can be used in the real world?
Why would you not care about hedging? The whole point of the risk neutral measure is that it goes hand in hand with the no-arbitrage theorem. If options are priced in such a way that there is no arbitrage possible, then they are priced with respect to a risk neutral measure. This also goes the other way: if they are not priced by a risk neutral measure (but e.g. directly by the physical measure) then there is an arbitrage opportunity. That's why we don't go with $\mu$.
Mar
24
comment Why the Black-Scholes formula can be used in the real world?
But the factor $m_{t,T}$ is defined as the measure change from the physical measure to the risk neutral measure, right? So saying that the risk neutral measure is just a convienent tool is a bit misleading, I would say. After all, the risk neutral measure determines the measure change $m_{t,T}$. Or am I missing something in your argument?
Mar
24
answered Euler discretization of Heston SDE in Mathematica
Jan
29
awarded  Commentator
Jan
29
comment What causes the call and put volatility surface to differ?
Interesting. Is it possible / feasible to use put-call parity as a constraint when calibrating your model to market data?
Dec
5
awarded  Yearling
Nov
17
comment How to price zero coupon bonds with the Monte Carlo method?
As a consistency check you could benchmark your generated paths against the exact solution. The error in the Euler scheme can grow quite quick for large discretizations, so it's good to know how well the distribution of the final points of the paths matches the exact distribution.
Nov
17
comment float64 to store price data: is precision sufficient?
Also, like rhaskett said, what you described in Option 1 is essentially how floating point numbers are stored.
Nov
17
comment float64 to store price data: is precision sufficient?
No, you're correct. NumPy does not support NaN for int types. Only for floats. Note that this is not some universal property of NaN's -- it was a choice made by the authors from NumPy not to support NaN for int.
Oct
26
comment Incompatibility of Lognormal Forward Model (LMM\BGM) and Lognormal Swap Model
Yea, you got it right. Swap rates and forward rates depend non-linearly on each other, so it would be quite weird to assume that both follow a lognormal distribution. If you try to derive $dS$ from (11) using (10), then there is no way you can end up with (12).