Quantitative Finance Collector is a blog on Quantitative finance analysis, methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management.

Nth much to say, for those of you interested into applying real option valuation model in real situation.

Doc file and Excel sheet can be downloaded here http://faculty.fuqua.duke.edu/~charvey/Teaching/BA456_2002/LogiTech/.

Spread option derives its value from the difference between the prices of two or more assets, it can be considered as a type of rainbow option in that it's payoff depends on 2 or 3 underlying assets. for instance, for a 2 underlying assets call spread option, the payoff is like max(S1 - S2 - K, 0), where K is the strike price betting on the spread (or difference) of these two stock prices. Spread option is widely used in energy industry, especially in oil industry.

In previous entry how to price spread option with Monte Carlo simulation was introduced, here is another valuation method of spread options follwing the article Low-Fat Spreads by K. Ravindran, RISK, Oct 1993.

for detail check http://www.mathfinance.org/FF/cpplib.php。

Cliquet option, also called ratchet option,  is an extended roll-down option, with strikes set at the barriers, which never knock out completely. It is a series of at the money options, with periodic settlement, resetting the strike value at the then current price level, at which time, the option locks in the difference between the old and new strike and pays that out as the profit. The profit can be accumulated until final maturity, or paid out at each reset date.

The Bates Model is a type of Jump-Difussion model that is able to improve calibration results for short term options. The Bates Model consists of Jumps processes built on top a Heston model.

http://www.javaquant.net/finalgo/BatesModel.html lists the C++ code to price Cliquet options using the Log-Jump variant of the Bates model with stochastic volatility.

Today is the Chinese traditional Mid-Autumn Festival, also known as the Moon Festival, which is used to celebrate the end of the summer harvesting season, first of all, wish you happy everyday and achieve what you want. A pic of Mooncake


Asian options are options where the payoff depends on the average price of the underlying asset during at least some part of the life of the option. The payoff from an average price call is max(Save - K, 0) where Save is the average value of the underlying asset calculated over a predetermined averaging period. Average price options are less expensive than regular options.

Besides anti-thetic sampling method, control variate is another popular way  for variance reduction, given the condition we can find a good proxy product, whose pricing formula is easy to get, in our case, geometric average asian option is used as control variate for arithemetic average asian option, here is a M file demonstrating Monte Carlo simulation on an arithmetic average price Asian option using a geometric average price Asian as control variate.

http://personal.strath.ac.uk/d.j.higham/ch22.m.

Constant maturity swap is a type of interest rate swap where the rate of interest of any single leg is readjusted in a periodic manner in case of market swap rate but not with the LIBOR (London Interbank Offered Rate) or any other floating reference index rate. In other words, it may also be said that the constant maturity swap actually allows the purchasers to fix the duration of the received flows on a swap. Constant maturity swap is also known as CMS. The Constant Maturity Swaps may be of two types - Single Currency Swaps or Cross Currency Swaps.

Pricing of cms option and a cms floor using the generalized Black-Scholes formula with a convexity adjustment Excel sample file: http://www.finmath.net/spreadsheets/CMS%20Option.zip, at the same page http://www.finmath.net/spreadsheets/ you can also find pricing of swaption using the generalized Black-Scholes formula.