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March 31st, 2017, 4:27 pm
Forum: Student Forum
Topic: simulate option prices time series data ?
Replies: 6
Views: 983

Re: simulate option prices time series data ?

I am curious how you can do Monte Carlo simulation of an option without simulating the underlying? I would never consider that, it would be needless complicated. Maybe I am not on the same page with you guys. In my mind, given initial stock  price S0, I simulate 1000 paths for the stock price, time...
March 31st, 2017, 5:10 am
Forum: Student Forum
Topic: simulate option prices time series data ?
Replies: 6
Views: 983

Re: simulate option prices time series data ?

What happens to the implied volatility during simulation? Will if stay at 20%. If so then you can simply compute the option price during every step of the simulation,  adjust the underlying and time to expiration after each step. Right now, volatility is supposed to be constant, i.e., stay at 20% a...
March 29th, 2017, 10:48 pm
Forum: Student Forum
Topic: simulate option prices time series data ?
Replies: 6
Views: 983

simulate option prices time series data ?

Suppose one call option contract with strike = 200 and expiration date 4/21/2017, and we are given stock price = 180, volatility = 20%, and interest rate = 3%. Under BS, we can compute call price using closed form solution. But, here I am talking about simulation (Monte Carlo or other simulation met...
March 6th, 2017, 5:52 pm
Forum: Student Forum
Topic: Heston delta closed form?
Replies: 14
Views: 1656

Heston delta closed form?

Under Heston model, European call = SP1 - Ke^(-rt)P2, I have read some papers which say that delta = P1. But by chain rule, delta = P1 + S*(dP1/dS) - Ke^(-rt)*(dP2/dS). My question is how the last two terms gone.  The integration part in dP1/dS and dP2/dS includes characteristic function f = exp{C +...
February 1st, 2017, 5:50 am
Forum: Student Forum
Topic: real data vs interpolated data ???
Replies: 10
Views: 1402

Re: real data vs interpolated data ???

Interesting. Do you use delta+gamma in your finite difference and backtest? 3 point central rule? And do you include theta when looking at delta changes? Is de delta better for longer maturities where gamma and theta are smaller? I used 5-point-stencil for finite difference method to compute dC/dK....
January 30th, 2017, 5:50 am
Forum: Student Forum
Topic: real data vs interpolated data ???
Replies: 10
Views: 1402

Re: real data vs interpolated data ???

When you compute dC/dS from dC/dK, does that method assume that the vol smile doesn't move when the stock price moves? I.e. dVol(K)/dS = 0? The assumption I am used is from Bates (2005) . Equation (1) on page 4, "it is assumed that the stochastic process of the underlying asset price exhibits const...
January 30th, 2017, 5:37 am
Forum: Student Forum
Topic: real data vs interpolated data ???
Replies: 10
Views: 1402

Re: real data vs interpolated data ???

I am reminded of this nice paper: http://edoc.hu-berlin.de/series/sfb-649-papers/2005-19/PDF/19.pdf which might be useful here. @Alan: would you please be more specific about how the paper you mentioned here connecting to delta? My guess: from the real options data, we can get arbitrage free IV, th...
December 6th, 2016, 8:52 pm
Forum: Student Forum
Topic: real data vs interpolated data ???
Replies: 10
Views: 1402

Re: real data vs interpolated data ???

When you compute dC/dS from dC/dK, does that method assume that the vol smile doesn't move when the stock price moves? I.e. dVol(K)/dS = 0? The assumption I am used is from Bates (2005) . Equation (1) on page 4, "it is assumed that the stochastic process of the underlying asset price exhibits const...
December 6th, 2016, 8:16 pm
Forum: Student Forum
Topic: real data vs interpolated data ???
Replies: 10
Views: 1402

real data vs interpolated data ???

To compute delta, I am considering to compute dC/dK using SPX index options data, then transfer to dC/dS. 5-point stencil will be used in the finite difference method to compute dC/dK, on a daily basis. And I do not care deep ITM options, which means I have two ways to to the calculation: first, rem...
November 2nd, 2016, 4:28 am
Forum: Numerical Methods Forum
Topic: Heston - Reference Prices
Replies: 37
Views: 24541

Re: Heston - Reference Prices

Sounds correct to me, with two caveats: -the arrow in the displayed figure should be pointing at the nodes in question. -with a fine enough time step, bottom nodes at the ex-date will lie below zero, which is why you must adopt a $\mathcal{D}(S)$ policy under the piecewise GBM model.  @Alan: Th...
October 26th, 2016, 8:32 pm
Forum: Numerical Methods Forum
Topic: Heston - Reference Prices
Replies: 37
Views: 24541

Re: Heston - Reference Prices

I would like to confirm the way to choose option value on ex-dividend date, when using bushy tree for one-time discrete dividend payment (not recombining, it is documented there are ways to make the tree recombining or use other more efficient methods, but let's talk about the bushy tree for now), u...
October 18th, 2016, 10:00 pm
Forum: Student Forum
Topic: Elasticity, what else?
Replies: 2
Views: 704

Elasticity, what else?

The term $$\dfrac{\partial^n f}{\partial x^n}\dfrac{x^n}{f^n}$$ is called elasticity when $n=1$. I am wondering what is the names for $n=2, 3, 4$, respectively.
September 2nd, 2016, 2:35 pm
Forum: Student Forum
Topic: Levy measure for Heston (1993) and Bates(1996)?
Replies: 6
Views: 1019

Re: Levy measure for Heston (1993) and Bates(1996)?

Sorry - I must have made a typo initially when I entered the parameters. I started from scratch and now get: call = 8.07652 put = 6.58771 which seems fairly close to the values in the paper you referenced. Thanks @LocalVolatility! I got what your got after finding some error in my codes! closed for...
September 1st, 2016, 11:25 pm
Forum: Student Forum
Topic: Levy measure for Heston (1993) and Bates(1996)?
Replies: 6
Views: 1019

Re: Levy measure for Heston (1993) and Bates(1996)?

Sorry, I cannot replicate your results. I get using my COS pricer:  call price = 7.15155061,  put price = 5.66274457. Are you sure you meant to use a mean jump size of -50% and a jump standard deviation of 4%? Sure you can use any values for testing but these seem unrealistic at least. Also have a ...
September 1st, 2016, 8:56 pm
Forum: Student Forum
Topic: Levy measure for Heston (1993) and Bates(1996)?
Replies: 6
Views: 1019

Re: Levy measure for Heston (1993) and Bates(1996)?

Thanks, Alan! This Helps. I am wondering who has code for the Bates (1996) model, so that he will run the code to check my codes is correct or not. Under risk neutral, the Bates (1996) model is $$d[ln S] = (r-\frac{1}{2}V)dt +\sqrt{V}dZ+dJ$$ $$dV=\alpha(m-V)dt+\sigma\sqrt{V}dW$$ $$dZdW =\rho dt$$ wh...

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