Google Quant Staff
[
2010/01/07 21:07 | by abiao ]
2010/01/07 21:07 | by abiao ]
Sharing a Google Quant Staff page I created initially for myself, the motivation was to make the job more convenient since I had to search in Google too many times per day, what's worse is sometimes I prefer video results, while sometimes what I need is just PDF documents or Matlab files. Adjusting frequently with Google advanced search makes me feel silk.
Google Quant Staff is by no means an invention, I just put several searching filters in one page, that's it.
For example, to find pdf documents about "Asian option", simply type "Asian option" in the form and click the PDF icon
Similarly each icon stands for one filter:
Searching results will be openned in a new browser window in Google as what I did was creating a page to filter results. You can also choose to search books in Amazon below.
PS: the page can also be used for keywords nothing to do with Quant staff as long as google catches them.
Anyway, hope you find it somehow useful: Google Quant Staff, bookmark if you like.
Google Quant Staff is by no means an invention, I just put several searching filters in one page, that's it.
For example, to find pdf documents about "Asian option", simply type "Asian option" in the form and click the PDF icon
Similarly each icon stands for one filter:
Searching results will be openned in a new browser window in Google as what I did was creating a page to filter results. You can also choose to search books in Amazon below.
PS: the page can also be used for keywords nothing to do with Quant staff as long as google catches them.
Anyway, hope you find it somehow useful: Google Quant Staff, bookmark if you like.
Vanna Volga Method
[ 2010/01/05 22:11 | by abiao ]
2010/01/05 22:11 | by abiao ]
The vanna volga method is a popular pricing model for implied volatilities, especially for foreign exchange options, it is an empirical procedure that can be applied to "draw" an implied volatility smile curve from three given quotes (reversal, ATM and butterfly) for a certan time to maturity. Empirical research shows the vanna volga method has a comparable pricing performance with some stochastic volatility model, for example, Castagna and Mercurio (2007) show the implied volatility curve of vanna volga method outperforms that of Malz (1997), and performs equally well as of SABR (2002).
By building a self-financing portfolio consisting a unit of option at strike K, -delta1 units of underlying asset, and -xi units of options at strike ki, Castagna and Mercurio (2007) calculate the weight xi for three given quotes with the help of Ito's lemma and then approximate the European option value under vanna volga method, as stated in the paper, VV pricing model has several advantages: "it has a clear financial rationale supporting, based on the hedging argument...; it allows for an automatic calibration to the main volatility data...; ... it can be extended to any European-style derivative..."
Below is a simple Matlab code to price a call option based on Castagna and Mercurio (2007):
where Vega is a function to compute vega under black scholes formula
Implied volatilities curve is therefore easily achieved by inverting VV pricing model. Interested ppl please refer to http://www.risk.net/risk/technical-paper/1506580/the-vanna-volga-method-implied-volatilities or an advanced one www.mathfinance.de/wystup/papers/wystup_vannavolga_eqf.pdf
By building a self-financing portfolio consisting a unit of option at strike K, -delta1 units of underlying asset, and -xi units of options at strike ki, Castagna and Mercurio (2007) calculate the weight xi for three given quotes with the help of Ito's lemma and then approximate the European option value under vanna volga method, as stated in the paper, VV pricing model has several advantages: "it has a clear financial rationale supporting, based on the hedging argument...; it allows for an automatic calibration to the main volatility data...; ... it can be extended to any European-style derivative..."
Below is a simple Matlab code to price a call option based on Castagna and Mercurio (2007):
% option price under Vanna volga model for any strike k
% sigma2 is ATM implied vol, k2 is ATM strike
s = 1.205;
t = 94/365;
r = -log(0.9902752)/t;
rf = -log(0.9945049)/t;
sigma1 = 0.0979;
sigma3 = 0.0929;
sigma2 = 0.09375;
k1 = 1.172;
k3 = 1.2504;
k2 = 1.2115;
k = 1.24;
Vega1 = Vega(s,k1,r,t,sigma2,rf);
Vega3 = Vega(s,k3,r,t,sigma2,rf);
Vegak = Vega(s,k,r,t,sigma2,rf);
x1 = Vegak*log(k2/k)*log(k3/k)/(Vega1*log(k2/k1)*log(k3/k1));
x3 = Vegak*log(k/k1)*log(k/k2)/(Vega3*log(k3/k1)*log(k3/k2));
price = blsprice(s,k,r,t,sigma2,rf)+x1*(blsprice(s,k1,r,t,sigma1,rf)...
-blsprice(s,k1,r,t,sigma2,rf))+x3*(blsprice(s,k3,r,t,sigma3,rf)...
-blsprice(s,k3,r,t,sigma2,rf));
% sigma2 is ATM implied vol, k2 is ATM strike
s = 1.205;
t = 94/365;
r = -log(0.9902752)/t;
rf = -log(0.9945049)/t;
sigma1 = 0.0979;
sigma3 = 0.0929;
sigma2 = 0.09375;
k1 = 1.172;
k3 = 1.2504;
k2 = 1.2115;
k = 1.24;
Vega1 = Vega(s,k1,r,t,sigma2,rf);
Vega3 = Vega(s,k3,r,t,sigma2,rf);
Vegak = Vega(s,k,r,t,sigma2,rf);
x1 = Vegak*log(k2/k)*log(k3/k)/(Vega1*log(k2/k1)*log(k3/k1));
x3 = Vegak*log(k/k1)*log(k/k2)/(Vega3*log(k3/k1)*log(k3/k2));
price = blsprice(s,k,r,t,sigma2,rf)+x1*(blsprice(s,k1,r,t,sigma1,rf)...
-blsprice(s,k1,r,t,sigma2,rf))+x3*(blsprice(s,k3,r,t,sigma3,rf)...
-blsprice(s,k3,r,t,sigma2,rf));
where Vega is a function to compute vega under black scholes formula
function VegaValue = Vega(s,k,r,t,sigma,rf)
d1 = (log(s/k)+(r-rf+0.5*sigma^2)*t)/(sigma*sqrt(t));
VegaValue = s*exp(-rf*t)*sqrt(t)*normpdf(d1,0,1);
d1 = (log(s/k)+(r-rf+0.5*sigma^2)*t)/(sigma*sqrt(t));
VegaValue = s*exp(-rf*t)*sqrt(t)*normpdf(d1,0,1);
Implied volatilities curve is therefore easily achieved by inverting VV pricing model. Interested ppl please refer to http://www.risk.net/risk/technical-paper/1506580/the-vanna-volga-method-implied-volatilities or an advanced one www.mathfinance.de/wystup/papers/wystup_vannavolga_eqf.pdf
Post your article on this blog
[ 2010/01/01 13:52 | by abiao ]
2010/01/01 13:52 | by abiao ]
Happy new year!
I have got few emails and messages recently asking for the possibility to write an article and post on Quantitative finance collector blog, for example, "I have come across finance sites and am willing to contribute with an article. Please do let me know if you are interested to do so", "I love to write unique finance articles & after seeing ur site I have written one unique article for ur site. Will u be interested to publish it in ur site along with my link"...
Forgive me if I didn't reply individually, the general answer is: YES, you can, but subject to the following criteria:
1, the content of the article must be relevant to quantitative finance in general, specifically, any article about quantitative trading, quantitative risk analysis, derivative pricing code and software, etc., is highly welcomed;
2, the article must be unique and writen only for Quantitative finance collector blog, instead of a copy from sites;
3, the site linked to must be healthy.
The benefits of posting artiles on this blog:
1, as a sign of gratitude, we will put a link back to your site in the post, which will increase the exposure and traffic of your site;
2, the link is do-follow, which means the link will be better recoganized by search engines;
3, more opinions on this blog is always good for our readers.
How to post an article:
simply send your article to abiao @ mathfinance.cn (remove space). Posting an article is totally free as we believe it will be a win-win strategy.
I have got few emails and messages recently asking for the possibility to write an article and post on Quantitative finance collector blog, for example, "I have come across finance sites and am willing to contribute with an article. Please do let me know if you are interested to do so", "I love to write unique finance articles & after seeing ur site I have written one unique article for ur site. Will u be interested to publish it in ur site along with my link"...
Forgive me if I didn't reply individually, the general answer is: YES, you can, but subject to the following criteria:
1, the content of the article must be relevant to quantitative finance in general, specifically, any article about quantitative trading, quantitative risk analysis, derivative pricing code and software, etc., is highly welcomed;
2, the article must be unique and writen only for Quantitative finance collector blog, instead of a copy from sites;
3, the site linked to must be healthy.
The benefits of posting artiles on this blog:
1, as a sign of gratitude, we will put a link back to your site in the post, which will increase the exposure and traffic of your site;
2, the link is do-follow, which means the link will be better recoganized by search engines;
3, more opinions on this blog is always good for our readers.
How to post an article:
simply send your article to abiao @ mathfinance.cn (remove space). Posting an article is totally free as we believe it will be a win-win strategy.
Friday reading list 12/25/09
[ 2009/12/25 16:18 | by abiao ]
2009/12/25 16:18 | by abiao ]
Have little time to read paper this week due to Christmas holiday, so only two are selected on this Friday's reading list:
1, Smile Dynamics IV. Recall we have collected the three simle dynamics paper by Lorenzo Bergomi, Quant of the Year 2008 awarded by Risk Magazine at lorenzo bergomi smile dynamics I, II and III, this is his fourth version. "In this paper we address the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. We introduce a new quantity, which we call the Skew Stickiness Ratio and show how, at order one in the volatility of volatility, it is linked to the rate at which the at-the-money-forward skew decays with maturity. We then focus on short maturity skews and (a) show that the difference between realized and implied SSR can be materialized as the P&L of an option strategy, (b) introduce the notion of realized skew." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1520443
2, What Drives Interbank Rates? Evidence from the Libor Panel. "The risk premium contained in the interest rates on three-month interbank deposits at large, internationally active banks increased sharply in August 2007 and risk premiahave remained at an elevated level since. This feature aims to identify the drivers of this increase, in particular the role of credit and liquidity factors." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1517680
1, Smile Dynamics IV. Recall we have collected the three simle dynamics paper by Lorenzo Bergomi, Quant of the Year 2008 awarded by Risk Magazine at lorenzo bergomi smile dynamics I, II and III, this is his fourth version. "In this paper we address the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. We introduce a new quantity, which we call the Skew Stickiness Ratio and show how, at order one in the volatility of volatility, it is linked to the rate at which the at-the-money-forward skew decays with maturity. We then focus on short maturity skews and (a) show that the difference between realized and implied SSR can be materialized as the P&L of an option strategy, (b) introduce the notion of realized skew." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1520443
2, What Drives Interbank Rates? Evidence from the Libor Panel. "The risk premium contained in the interest rates on three-month interbank deposits at large, internationally active banks increased sharply in August 2007 and risk premiahave remained at an elevated level since. This feature aims to identify the drivers of this increase, in particular the role of credit and liquidity factors." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1517680
Happy Christmas 2009
[ 2009/12/23 15:05 | by abiao ]
2009/12/23 15:05 | by abiao ]
Christmas & New Year are around the corner, many thanks for your visit and support www.mathfinance.cn in 2009, Wish all of you healthy & wish a quick recovery of global Quant market.
Good good study, Day day up, a song Christmas With a Capital "C"
Good good study, Day day up, a song Christmas With a Capital "C"
