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by LocalVolatility
November 4th, 2014, 7:48 am
Forum: Student Forum
Topic: when to pay rebate in barrier option?
Replies: 3
Views: 3292

when to pay rebate in barrier option?

It depends on the contractual terms but both types are possible and actually traded.
by LocalVolatility
October 31st, 2014, 9:11 am
Forum: Numerical Methods Forum
Topic: Optimization for hedging portfolio
Replies: 5
Views: 3934

Optimization for hedging portfolio

<t>I handle constraints by the bounce-back method described on p. 204ff inPrice, Kenneth V. and Rainer M. Storn and Jouni A. Lampinen (2005) "Differential Evolution - A Practical Approach to Global Optimization", Springer.I constrain the initial population to lie in the feasible region by simply re-...
by LocalVolatility
October 31st, 2014, 8:47 am
Forum: Numerical Methods Forum
Topic: MC for Boundary Exercise American Option
Replies: 1
Views: 3514

MC for Boundary Exercise American Option

Longstaff, Francis A. and Eduardo S. Schwartz (2001) "Valuing American Options by Simulation: A Simple Least-Squares Approach", Review of Financial Studies, Vol. 14, No. 1, pp. 113-147
by LocalVolatility
October 31st, 2014, 7:52 am
Forum: Student Forum
Topic: No Arbitrage Pricing Puzzle
Replies: 8
Views: 3862

No Arbitrage Pricing Puzzle

<t>Its a complete shot in the dark as I am not that familiar with commodity models but two aspects you might want to consider:(i) The no-arbitrage relationship you mention requires that the spot asset is tradable. The futures price then follows from the spot price. The other way around doesn't seem ...
by LocalVolatility
October 29th, 2014, 8:25 am
Forum: Student Forum
Topic: Double barrier options (discrete/continuous monitoring)
Replies: 13
Views: 5224

Double barrier options (discrete/continuous monitoring)

<t>For the discretely monitored case: You can easily get closed-form solutions using higher-order binary options. The continuously monitored case can be also approached with the method of images. The main references are (there is some overlap between the papers):Buchen, Peter W. (2001) "Q-Options an...
by LocalVolatility
October 28th, 2014, 11:56 am
Forum: Numerical Methods Forum
Topic: Optimization for hedging portfolio
Replies: 5
Views: 3934

Optimization for hedging portfolio

<t>QuoteBTW what do think of DE/rand/1/bin versus DE/best/2/bin?As the choice doesn't seem so obvious to me, I usually employ a self-adaptive algorithm to learn the optimal mutation strategy. I.e. you randomize the choice over different schemes with certain probabilities (e.g. start with equal) and ...
by LocalVolatility
October 28th, 2014, 10:09 am
Forum: Student Forum
Topic: Carr Madan approach with continuously paid dividend
Replies: 2
Views: 3159

Carr Madan approach with continuously paid dividend

<t>The short explanation: You are pricing European options whose payoff only depends on the terminal distribution of the underlying asset price. For a fixed initial spot price, increasing the dividend yield simply shifts the mean of the distribution down. This is equivalent to not adjusting the dist...
by LocalVolatility
October 24th, 2014, 7:31 am
Forum: Numerical Methods Forum
Topic: Optimization for hedging portfolio
Replies: 5
Views: 3934

Optimization for hedging portfolio

<t>If you think that your fit is bad because your routine gets trapped in the wrong optimum, then I'd recommend you have a look at heuristic optimization routines. My workhorse is differential evolution. It is of course significantly slower than other routines as they require quite a high number of ...
by LocalVolatility
October 20th, 2014, 1:52 pm
Forum: Trading Forum
Topic: Black Scholes Model which Volatilty to use
Replies: 1
Views: 3430

Black Scholes Model which Volatilty to use

<t>Are you asking whether you should use a per annum or a per day volatility as an input to the Black and Scholes formula? It depends.. It just has to be consistent with the unit that you measure time in. I.e. if your time-to-expiry is in years (as is commonly the case) then you use a per annum vola...
by LocalVolatility
October 14th, 2014, 12:16 pm
Forum: Technical Forum
Topic: FX option volatility
Replies: 4
Views: 4529

FX option volatility

Have a look at:Reiswich, Dimitri (2010) "The Foreign Exchange Volatility Surface", PhD DissertationReiswich, Dimitri and Uwe Wystup (2012) "FX Volatility Smile Construction", Wilmott MagazineWystup, Uwe (2006) "FX Options and Structured Products", Wiley
by LocalVolatility
October 9th, 2014, 11:14 am
Forum: General Forum
Topic: Shortest Proof Mean-Variance Efficiency
Replies: 3
Views: 3630

Shortest Proof Mean-Variance Efficiency

The proof is in Merton (1972) "An Analytical Derivation of the Efficient Portfolio Frontier", Journal of Financial and Quantitative Analysis.Also have a look at Feldman and Reisman (2003) "Simple Construction of the Efficient Frontier", European Financial Management.
by LocalVolatility
April 25th, 2013, 1:25 pm
Forum: Student Forum
Topic: Two period Binomial Model with interest
Replies: 3
Views: 7649

Two period Binomial Model with interest

<t>I can see a few problems in both approaches. First, notice that the up and down move of the stock is a constant USD amount but not a constant percentage. Consequently, you need to recompute the risk-neutral probabilities at each of the three nodes - they change. Next, to find the option value in ...
by LocalVolatility
April 25th, 2013, 2:51 am
Forum: Student Forum
Topic: forward contract pricing
Replies: 2
Views: 7596

forward contract pricing

<t>Hi,you end up with the correct formula for the value in the last line although [$]F_{t_1}[$] is not given by the formula in the line before. You should make sure you understand where these expressions come from and the best way to do so is to carefully write down the cash-flows. Assume you took a...
by LocalVolatility
April 7th, 2013, 1:42 am
Forum: Student Forum
Topic: Do banks use Black-Scholes to price options?
Replies: 5
Views: 8743

Do banks use Black-Scholes to price options?

<t>From my experience: yes and no.When it comes to plain vanilla options, then usually yes for pricing purposes. Banks usually have a system that constantly fits some parametric form or model to the Black-Scholes implied volatility smiles for the different maturities. When it then comes to quoting p...
by LocalVolatility
March 17th, 2013, 12:28 pm
Forum: Student Forum
Topic: "r" in the 1973 Black Scholes model
Replies: 5
Views: 8320

"r" in the 1973 Black Scholes model

You use the continuously compounded rate.
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