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by VivienB
September 22nd, 2015, 7:43 am
Forum: Student Forum
Topic: Shifted Log Normal Model Vs Bachelier Model
Replies: 19
Views: 5411

Shifted Log Normal Model Vs Bachelier Model

<t>QuoteOriginally posted by: DeepakKumarThanks all for sharing your thoughts on this. Still I have a doubt, how to get the size of the shift, I mean (consider I have negative rates so that Black is no more an option) do I need to calibrate for the size of shift still I get the solution from shifted...
by VivienB
September 22nd, 2015, 6:58 am
Forum: Student Forum
Topic: Shifted Log Normal Model Vs Bachelier Model
Replies: 19
Views: 5411

Shifted Log Normal Model Vs Bachelier Model

<t>QuoteOriginally posted by: list1/// I doubt that Bachelier studied the equation when b = 0 dS (t) = lamda S (0)) z (t)^0.5 dW (t)My points are about the shifted Black model. The article (about shifted Heston) is just an example of the use of the same kind of shifted model parametrisationQuoteOrig...
by VivienB
September 19th, 2015, 10:18 am
Forum: Student Forum
Topic: Shifted Log Normal Model Vs Bachelier Model
Replies: 19
Views: 5411

Shifted Log Normal Model Vs Bachelier Model

<t>QuoteOriginally posted by: list1log-shifting model from your reference is defined by eq at the bottom of the p53dF(t; T,S) = σ(t; T,S) [ F(t; T,S) − a] dW(t)which is specifies forward-rate dynamics in the shifted lognormal model. The eq presented by VivienB is of the. Risk term dependence on S ( ...
by VivienB
September 18th, 2015, 3:29 pm
Forum: Student Forum
Topic: Shifted Log Normal Model Vs Bachelier Model
Replies: 19
Views: 5411

Shifted Log Normal Model Vs Bachelier Model

<t>QuoteOriginally posted by: bearishQuoteOriginally posted by: VivienB- Bachelier is a particular case of shifted log normal. Then it is not strictly better but at least it can't be worse.- Shifted log normal allows to match atm + skew near atm, whereas Bachelier allow to match only atm.Bachelier i...
by VivienB
September 17th, 2015, 2:31 pm
Forum: Student Forum
Topic: Shifted Log Normal Model Vs Bachelier Model
Replies: 19
Views: 5411

Shifted Log Normal Model Vs Bachelier Model

- Bachelier is a particular case of shifted log normal. Then it is not strictly better but at least it can't be worse.- Shifted log normal allows to match atm + skew near atm, whereas Bachelier allow to match only atm.
by VivienB
August 31st, 2015, 8:23 am
Forum: Numerical Methods Forum
Topic: Heston model calibration
Replies: 19
Views: 9259

Heston model calibration

Cuchulainn,I simply modify the function so that it returns a high value when the parameters are out of the domain. Edit: it could be refined by choosing an initial population that lies inside your domain.
by VivienB
August 27th, 2015, 3:43 pm
Forum: Numerical Methods Forum
Topic: Heston model calibration
Replies: 19
Views: 9259

Heston model calibration

<t>There are some nice tricks on the DE page, in particular the random choice of F at each generations (see the Practical Advice part).I use DE for almost all models, including Bates.For Heston, the calibration time is only a few secs. If it can help, I use a vega weighted error on the prices, + a w...
by VivienB
May 4th, 2015, 2:47 pm
Forum: General Forum
Topic: Volatility surface smoothing
Replies: 5
Views: 5892

Volatility surface smoothing

<t>A good approach is to perform SVI interpolation per maturity to compute call prices on a cartesian grid (on strikes or log strikes), then use Andreasen, Huge, Volatility Interpolation to fill the gaps between maturities. It will leads to a complete and arbitrage free implied (or local) volatility...
by VivienB
March 23rd, 2015, 11:34 am
Forum: Student Forum
Topic: The Heston Model and a positive Rho? Possible?
Replies: 8
Views: 3806

The Heston Model and a positive Rho? Possible?

This is not surprising for FX as the Heston rho for C1/C2 is minus the rho for C2/C1 => at least one rho is >=0.However, your volatilities seem to have a negative skew (on the graph), then one would expect a negative rho.
by VivienB
March 3rd, 2015, 2:42 pm
Forum: Student Forum
Topic: Analytical prices in a (swap rate based) SABR model
Replies: 2
Views: 3095

Analytical prices in a (swap rate based) SABR model

<t>What you are trying to price is a CMS caplet. Hagan wrote also an article for that: Convexity Conundrums: Pricing CMS Swaps, Caps, and Floors.The idea is to approximate the zero coupon as a function of the swap rate, then [$]A(t) = a(S(t))[$] and the price is [$]A(0)E_A[f(S(t)][$], that can be co...
by VivienB
January 15th, 2015, 7:57 am
Forum: General Forum
Topic: SVI term structure
Replies: 5
Views: 4580

SVI term structure

QuoteI know the raw SVI (only fit the smile/skew for a given maturity) is not arb-free with butterfly arbitrage(Axel Vogt counterexample).That's what I meant when I said that SVI vol is not arbitrage free.
by VivienB
January 14th, 2015, 8:58 am
Forum: General Forum
Topic: SVI term structure
Replies: 5
Views: 4580

SVI term structure

<t>I'm not sure there is (another) simple ways to interpolate IV between maturities, that is why the authors wrote this article.Moreover, the proposed methodology can be used with SVI fitting (and that's how I personally use it):Step 1 Fit SVI for each quoted maturities T_iStep 2 interpolate the IV ...
by VivienB
January 13th, 2015, 3:53 pm
Forum: General Forum
Topic: SVI term structure
Replies: 5
Views: 4580

SVI term structure

You can use this article (Andreasen, Huge, Volatility Interpolation) to interpolate IV without arbitrage.
by VivienB
November 3rd, 2014, 8:15 am
Forum: Student Forum
Topic: No Arbitrage Pricing Puzzle
Replies: 8
Views: 4484

No Arbitrage Pricing Puzzle

<t>Assume that the storage cost is [$]c S(t)\delta t[$] between [$]t[$] and [$]t + \delta t[$]. Paying this storage cost is equivalent to receive a negative dividend [$]-c S(t)\delta t[$].Then, the forward is [$] e^{(r - (-c))t}S(0) = e^{(r + c)t}S(0)[$].The form of the storage cost can be a more co...
by VivienB
October 31st, 2014, 3:09 pm
Forum: Student Forum
Topic: No Arbitrage Pricing Puzzle
Replies: 8
Views: 4484

No Arbitrage Pricing Puzzle

Your hypothesis " there are no storage costs associated with the underlying " is in contradiction with your assumed dynamic for S (no storage cost + no dividends + ... => dS = rS dt + O(dW)). Hence it is normal to leads to other contradictions.
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