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by LocalVolatility
April 1st, 2015, 5:03 pm
Forum: Technical Forum
Topic: Adjustment of Local Vol model
Replies: 2
Views: 2899

Adjustment of Local Vol model

Sorry for the unconstructive comment - I couldn't resist..QuoteBy "close enough" I mean something of the order of 50bps for a 6 year index linked productSo we now have a lower bound of your institution's margin on these types of deals. ;-)
by LocalVolatility
March 19th, 2015, 7:29 am
Forum: General Forum
Topic: How to price European put option with short selling cost?
Replies: 2
Views: 3032

How to price European put option with short selling cost?

(1) Yes, you can price the repo like a continuous dividend yield.(2) The same holds true for calls as you are able to receive the repo on you long position.(3) So by (2) it makes no difference.
by LocalVolatility
March 16th, 2015, 1:02 pm
Forum: Technical Forum
Topic: Distribution of max BM - BM
Replies: 16
Views: 3998

Distribution of max BM - BM

<t>Let [$]M_t = \max_{0 \leq u \leq t} W_u[$]. You know that [$]M_t[$] and [$]W_t[$] have the joint density[$]f_{M_t, W_t}(m, w) = \frac{2 (2m - w)}{t \sqrt{2 \pi t}} \exp \left\{ -\frac{(2m - w)^2}{2 t} \right\}[$]. Then I'd just take it from there..[$]\mathbb{P} \left\{ M_t - W_t \geq x \right\} =...
by LocalVolatility
March 16th, 2015, 7:55 am
Forum: Technical Forum
Topic: DVega/DSpot
Replies: 4
Views: 3775

DVega/DSpot

QuoteDo you have the same graph for a Down-in put by any chance?Try to generate it yourself. A down-and-in put is just a plain vanilla put minus a down-and-out put.
by LocalVolatility
March 16th, 2015, 7:49 am
Forum: Technical Forum
Topic: Local Vol vs Implied Vol surface
Replies: 6
Views: 3868

Local Vol vs Implied Vol surface

<t>QuoteNow, if you construct the local volatilities in order to perfectly match the reference plain vanilla prices, the local and implied volatilities should be the same, aren't they? Since the volatility is the only factor i am solving for, am I right?Unfortunately not.Think of the local volatilit...
by LocalVolatility
March 12th, 2015, 7:40 am
Forum: Technical Forum
Topic: Local Vol vs Implied Vol surface
Replies: 6
Views: 3868

Local Vol vs Implied Vol surface

<t>See e.g. Dupire, Bruno (1994) "Pricing With a Smile", Risk Magazine, Vol. 17, No. 1, pp. 18-20 for the original reference of how to extract the local volatility surface from an implied volatility surface (or equivalently from a continuum of European plain vanilla call options). Also have a look a...
by LocalVolatility
March 11th, 2015, 8:25 am
Forum: Technical Forum
Topic: Local Vol vs Implied Vol surface
Replies: 6
Views: 3868

Local Vol vs Implied Vol surface

<t>I am not too sure I understand your question correctly..If you are asking whether the local volatility (of a calibrated model) at a given strike and maturity matches the market implied volatility (that the model has been calibrated to), then the answer is in general no. An exception is for exampl...
by LocalVolatility
March 11th, 2015, 8:16 am
Forum: Technical Forum
Topic: DVega/DSpot
Replies: 4
Views: 3775

DVega/DSpot

<t>If you are in the standard Black and Scholes setting with a single volatility, then when the strike of a down-and-out put is significantly above the barrier (relative to the volatility and maturity) the holder of a long position is vega long near the strike and vega short slightly above the barri...
by LocalVolatility
February 13th, 2015, 11:03 am
Forum: General Forum
Topic: fast calculation of BS implied volatility
Replies: 8
Views: 4426

fast calculation of BS implied volatility

<t>QuoteI prefer this paper by Minqiang Li from 2006I second this. Go forLi, Minqiang (2008) "Approximate Inversion of the Black-Scholes Formula Using Rational Functions', European Journal of Operations Research, Vol. 185, No. 2, pp. 743-759if you need a good initial guess and then add a few Newton-...
by LocalVolatility
February 2nd, 2015, 4:30 pm
Forum: Student Forum
Topic: A question on probabilities
Replies: 2
Views: 3233

A question on probabilities

<t>The solution can be expressed analytically using higher-order binary options. The usefulness of this is limited though as monthly observations with two years to maturity will yield a solution in terms of a 24-dimensional normal distribution function.See the references that I gave in this post for...
by LocalVolatility
February 2nd, 2015, 9:39 am
Forum: Student Forum
Topic: Arbitrage-free implied volatility surface - Introduction
Replies: 1
Views: 2991

Arbitrage-free implied volatility surface - Introduction

Continue reading Section 2. The arbitrage opportunities in Figure 1 come from violations of the monotonicity and/or convexity requirements.
by LocalVolatility
December 24th, 2014, 9:02 am
Forum: Student Forum
Topic: Example dataset (with 'results') for Heston Calibration
Replies: 2
Views: 3093

Example dataset (with 'results') for Heston Calibration

What about using some reasonable parameters to generate a volatility surface and see if your fitting routine can recover the original parameters.If you want to have reference values to check your pricing routine, then you could for example use QuantLib.
by LocalVolatility
December 4th, 2014, 1:14 pm
Forum: Student Forum
Topic: Risk-neutral probability measure
Replies: 7
Views: 3214

Risk-neutral probability measure

<t>Not quite.. I assume the [$]X_i[$] are uncorrelated Brownian motions, then one of the diffusion terms should be different. Plus, you already seemed to have jumped to some other measure as the drifts changed.ByQuoteHint: Start by rewriting their dynamics in terms of independent Brownian motions fi...
by LocalVolatility
December 4th, 2014, 6:39 am
Forum: Student Forum
Topic: Risk-neutral probability measure
Replies: 7
Views: 3214

Risk-neutral probability measure

<t>I assume this is homework? Nothing special here really.. If you are only interested in finding the risk-neutral probability measure, then you can ignore all the part about the asset [$]V[$] and just find an equivalent probability measure [$]\mathbb{P}^*[$] such that both discounted primary asset ...
by LocalVolatility
November 5th, 2014, 4:25 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3780

density of sv-model with jumps

<t>Given the characteristic function of the logarithmic returns [$]\ln \left( S_t / S_0 \right)[$], you can use the COS method to obtain the implied distribution. The computation can be neatly vectorized. SeeFang, Fang and Cornelis W. Oosterlee (2008) "A Novel Pricing Method for European Options Bas...
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