Sunday, September 22, 2013
Saturday, September 21, 2013
Recently I've got to refresh MPT knowledge and hence there are few references to share.
MPT and Markowitz Model
Sunday, September 15, 2013
Thousands of people in financial industry are explicitly involved in financial trading all over the world. Hundreds of thousands are involved implicitly. Based on my experience the percentage of people consciously doing their job is not high. Nevertheless it is highly important to understand at least the high level principles of process happening behind the scenes of financial institution when a trade is done.
Who Works on the Trade?
First, it is necessary to understand what stakeholders work with the trade during its life.
Trade Info Structure
Below you can find a sample of trade attributes structured into different categories (the trade is not real):
- Identifier: E54123
- Asset class: Equity
- Type: Spot
- Status: Awaiting confirmation
- Trade date: 3 June 2009
- Transaction time: 11:09 GMT+1
- Transaction location: London
- Buy or Sell: Buy
- Notional: 20 000
- Ticker: CAD
- Exchange: LSE
- Currency: GBP
- Price: 15.27p
- Salesperson: Elizabeth Smith
- Sales credits: 150
- Jurisdiction: UK
- Desk: Equity trading
- Trader: John Baker
- Assistant: Mark Eton
- Trading book: GBP Equity trading
- Counterparty: The Bank Address: Liverpool st, London
- Payment Type: SWIFT
- Payment Code: UIT TRY XXX
- Counterparty reference: LCE1985-04B
- Settlement Date: 5 June 2009
- Trade date: 15 June 2009
- Settlement date: 17 June 2009
- Maturity date: 15 Sep 2009
Different stakeholders work with the trade at different time. This is similar to a conveyor at a plant.
BackgroundMajor break-through in the valuation of derivatives came with two finance professors at MIT, Black and Scholes, came out with a formula that related the price of a call option to the price of the stock to which the option applies. Even though the model is not used by financial institutions today it still contains ideas that used in financial modelling.
The Black-Scholes formula is a partial differential equation that can be used to price the present value of an option under certain assumptions. The equation describes the Markov process of underlying asset price and it looks as given below:
Monte Carlo SimulationAssuming the Brownian motion over this short period will be a normal (Gaussian) distribution with a mean of 0 and a variance of the time interval the iterative formula will be as follows:
Below you can find an implementation of Monte Carlo simulation of option pricing in python.
The program will generate a number of asset price paths. At option expiry time obviously the price will differ. Option price then will be the average of all gains received at expiry time.
- J.Hull Futures, Options and Other Derivatives