SERVING THE QUANTITATIVE FINANCE COMMUNITY

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by LocalVolatility
January 20th, 2016, 11:21 am
Forum: Book And Research Paper Forum
Topic: Good book for the implementation of Quantitative Finane Models
Replies: 5
Views: 4836

Good book for the implementation of Quantitative Finane Models

I own the book by Kienitz and Wetterau that you mention and can strongly recommend it - very hands-on.
by LocalVolatility
January 5th, 2016, 9:01 am
Forum: Technical Forum
Topic: Sign of shares number in BS portfolio
Replies: 21
Views: 3353

Sign of shares number in BS portfolio

<t>Have a look at the paperBergman, Yaacov Z., Bruce D. Grundy, and Zvi Wiener (1996) "General Properties of Option Prices", Journal of Finance, Vol. 51, No. 5, pp. 1573-1610They show that under fairly general one- and two-dimensional diffusion processes, the delta of a European claim with non-decre...
by LocalVolatility
September 22nd, 2015, 12:17 pm
Forum: Numerical Methods Forum
Topic: Risk-neutral random walk monte carlo simulation
Replies: 11
Views: 5143

Risk-neutral random walk monte carlo simulation

The first discretization generates normally distributed [$]S_t[$] (i.e. it can become negative). The second is equivalent to discretizing the SDE for [$]\ln \left( S_t \right)[$] which follows a constant coefficient arithmetic Brownian motion and thus there is no discretization error.
by LocalVolatility
September 22nd, 2015, 6:18 am
Forum: Student Forum
Topic: Conditional Expected First Hitting Time
Replies: 14
Views: 2575

Conditional Expected First Hitting Time

<t>Thank you Alan.I was already using the Brownian bridge correction for the hitting probability between two simulated spots that both don't breach the barrier. My problem was correctly simulating the hitting times. I will try your suggestions a) and b) see how they compare to the analytical solutio...
by LocalVolatility
September 21st, 2015, 3:00 pm
Forum: Student Forum
Topic: Conditional Expected First Hitting Time
Replies: 14
Views: 2575

Conditional Expected First Hitting Time

<t>Thanks outrun and Cuchulainn for the replies.As outrun said, I am indeed looking for a way to correct the hitting time in my MC simulation. I am using that MC simulation to validate my FD implementation. The contract that I am valuing is more complex than just the one-touch case that I was asking...
by LocalVolatility
September 21st, 2015, 10:50 am
Forum: Student Forum
Topic: Conditional Expected First Hitting Time
Replies: 14
Views: 2575

Conditional Expected First Hitting Time

<t>Hi,this is probably a well-known problem but I seem to be searching for the wrong keywords.Consider a constant coefficient geometric Brownian motion for the stock price. I am trying to value a one-touch binary option with a rebate at-hit through Monte Carlo simulation. I know there exist closed-f...
by LocalVolatility
August 26th, 2015, 8:07 pm
Forum: Technical Forum
Topic: Test if correct output on FFT Bates
Replies: 14
Views: 3935

Test if correct output on FFT Bates

I can't tell you the exact precision of the reference values that I gave you. But the error should be less than 1.0e-04. This is the tolerance that I use in my unit tests against the QuantLib values.
by LocalVolatility
August 26th, 2015, 6:26 pm
Forum: Technical Forum
Topic: Test if correct output on FFT Bates
Replies: 14
Views: 3935

Test if correct output on FFT Bates

<r>One more suggestion: You mentioned that you use MATLAB. Check the book by Kienitz and Wetterau - its very hands on and implementes the COS method. See <URL url="http://www.mathworks.com/matlabcentral/profile/authors/3467507-kienitz-wetterau-finmodelling"><LINK_TEXT text="http://www.mathworks.com/...
by LocalVolatility
August 26th, 2015, 6:13 pm
Forum: Technical Forum
Topic: Test if correct output on FFT Bates
Replies: 14
Views: 3935

Test if correct output on FFT Bates

<r>Here are my reference prices for the market data you gave in your last post. I do not have an implementation of the SVJJ model.========== HESTON ==========strike = 700.00, price = 625.00006285strike = 800.00, price = 525.00127652strike = 900.00, price = 425.01690315strike = 1000.00, price = 325.1...
by LocalVolatility
August 26th, 2015, 10:45 am
Forum: Technical Forum
Topic: Test if correct output on FFT Bates
Replies: 14
Views: 3935

Test if correct output on FFT Bates

I get using the COS method:strike = 1298.70 --> price = 47.2426strike = 1701.50 --> price = 0.0349By the way - you could use QuantLib to generate some reference prices to test your implementation.
by LocalVolatility
July 22nd, 2015, 8:57 am
Forum: Numerical Methods Forum
Topic: Heston model calibration
Replies: 19
Views: 7890

Heston model calibration

<r>I second Alan's recommendation to check your Heston pricer implementation first. Build some unit tests using publicly available test cases - I use e.g. the ones here <URL url="http://wilmott.com/messageview.cfm?catid=34&threadid=90957"><LINK_TEXT text="http://wilmott.com/messageview.cfm?cati ...
by LocalVolatility
July 16th, 2015, 1:07 pm
Forum: Student Forum
Topic: Partial time double barrier (binary) option
Replies: 1
Views: 2221

Partial time double barrier (binary) option

<t>You can price a deferred start double barrier option (with continuous barrier) in closed-form (as an infinite sum over 2-dimensional binary options) using the method of images. All you need is in Konstandatos, Otto (2008) "Pricing Path Dependent Exotic Options: A Comprehensive Mathematical Framew...
by LocalVolatility
July 16th, 2015, 7:55 am
Forum: Book And Research Paper Forum
Topic: Essential practitioner books in quant finance
Replies: 4
Views: 5790

Essential practitioner books in quant finance

<t>One of the books that I regularly use as a reference isKienitz, Joerg and Daniel Wetterau (2012) "Financial Modelling: Theory, Implementation and Practice with MATLAB Sources"The book covers a wide range of current topics from a practitioners perspective. I especially found the chapters on transf...
by LocalVolatility
May 19th, 2015, 4:19 pm
Forum: Student Forum
Topic: Cumulant transform in BNS model
Replies: 29
Views: 5271

Cumulant transform in BNS model

<t>I once worked this out (read: "had Mathematica do most of the work") for the case where the Levy subordinator is a gamma Ornstein-Uhlenbeck process. See the attached extract from my notes.A few remarks regarding the notation: [$]\tilde{X}_t[$] defined such that under the risk-neutral probability ...
by LocalVolatility
April 1st, 2015, 5:07 pm
Forum: General Forum
Topic: Expected P&L of Delta Hedging in BS
Replies: 4
Views: 3284

Expected P&L of Delta Hedging in BS

For non-constant volatility see e.g. El Karoui, Jeanblanc and Shreve (1998) "Robustness of the Black and Scholes Formula", Mathematical Finance, Vol. 8, No 2.
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