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by Arthurim
August 25th, 2017, 10:54 am
Forum: Student Forum
Topic: Kirk's approximation
Replies: 4
Views: 2282

Re: Kirk's approximation

I know the formula, I am just looking for Kirk's original paper.
by Arthurim
August 25th, 2017, 10:53 am
Forum: Student Forum
Topic: Higher order greeks: Vomma, Ultima and Totto
Replies: 0
Views: 1966

Higher order greeks: Vomma, Ultima and Totto

I came across those higher order greeks: Vomma, Ultima and Totto.
I was wondering: when would one use them? Who is interested in monitoring these greeks? For what products are they important ?
by Arthurim
August 25th, 2017, 10:49 am
Forum: Student Forum
Topic: Close form formula vs Simuations
Replies: 57
Views: 17054

Close form formula vs Simuations

When pricing an option we often have the choice between using a close-form formula or running MC simulations.
What are the pros and the cons of each one ?
How do you choose which one to use ?
by Arthurim
August 24th, 2017, 9:17 am
Forum: Student Forum
Topic: Kirk's approximation
Replies: 4
Views: 2282

Kirk's approximation

Hi, I am looking for Kirk's paper E. “Correlations in the energy markets, in managing energy price risk.” 1995. I haven't been able to find it on the internet though a lot of people refer to it in their paper. I know the approximation but I am curious and would like to read Kirk's paper. Do you know...
by Arthurim
August 15th, 2017, 3:59 pm
Forum: Student Forum
Topic: Monte Carlo pricing
Replies: 6
Views: 2379

Re: Monte Carlo pricing

Thank you outrun, I finally derived it by myself (took some time though).
I did some basic sto calculus in the past, but have to admit that I forgot a little bit.
by Arthurim
August 15th, 2017, 3:48 pm
Forum: Student Forum
Topic: How to price a spread option on strategies involving more than two different prices ?
Replies: 13
Views: 3462

Re: How to price a spread option on strategies involving more than two different prices ?

Finally found a generalisation of the Kirk's approximation for multi asset spread options ( paper ). Similarly, if we have N prices $$max(0,F_N-\sum_{k=1}^{N-1}F_k-K)$$ translates into $$F_N N(d_1)-(\sum_{k=1}^{N-1}F_k+K)N(d_2)$$ But then what if we have  [$]max(0,F_N+F_{N-1}-\sum_{k=1}^{N-2}F_k-K)[...
by Arthurim
August 11th, 2017, 10:28 am
Forum: Student Forum
Topic: Monte Carlo pricing
Replies: 6
Views: 2379

Re: Monte Carlo pricing

Thanks a lot, where can I find the proof of that simulation formula ?
by Arthurim
August 11th, 2017, 10:23 am
Forum: Student Forum
Topic: MCS with correlated Brownian motions
Replies: 0
Views: 1650

MCS with correlated Brownian motions

We denote by [$]F(t_i, t_j)[$] the forward price for delivery day [$]t_j[$] observed on date [$]t_i[$].     $$F(t_i, t_j)=F(0, t_j)\exp\left(-\frac{1}{2}\sigma(t_i,t_j)^2t_i+\sigma(t_i,t_j)W(t_i,m)\right)$$     where     - [$]m[$] is the month containing period [$]t_j[$]     -[$]\sigma(t_i, t_j)[$] ...
by Arthurim
August 11th, 2017, 10:19 am
Forum: Student Forum
Topic: Monte Carlo pricing
Replies: 6
Views: 2379

Re: Monte Carlo pricing

Thank you outrun.
What if it is not a stock but an asset whose price can go below 0 ? (modelised with an OU process for example)
Is there something more accurate than the Euler discretisation ?
by Arthurim
August 11th, 2017, 9:33 am
Forum: Student Forum
Topic: How to price a spread option on strategies involving more than two different prices ?
Replies: 13
Views: 3462

Re: How to price a spread option on strategies involving more than two different prices ?

Thank you all for your answers. outrun: I am not familiar with moment matching methods, but from what I found, I believe I will try the quasi MC. forolloos: Thank you for the paper, I had the intuition for the generalization of Kirk's approximation but did not know whether this was really working an...
by Arthurim
August 11th, 2017, 9:23 am
Forum: Student Forum
Topic: Monte Carlo pricing
Replies: 6
Views: 2379

Monte Carlo pricing

Hi all, I am very new to MC simulations for pricing. If we define the price process for a given asset by: $$dS=\mu S_t dt+ \sigma S_tdW_t$$ does it mean that at a given time time t we have the following ? $$S_t=S_{t-1}+dS=S_{t-1}(1+(\mu dt + \sigma dW_t))=S_0(1+(\mu dt + \sigma dW_t))^t$$ Then, if I...
by Arthurim
August 10th, 2017, 1:09 pm
Forum: Student Forum
Topic: How to price a spread option on strategies involving more than two different prices ?
Replies: 13
Views: 3462

How to price a spread option on strategies involving more than two different prices ?

To price a simple spread option, one can use Kirk's approximation combined with Margrabe's formula as a close form formula if you have two different prices in the payoff of your option. But what if you have more than 2 prices ? Is there any close form formula ? Else how would you price it ? $$\matho...