By Sunil K Parameswaran
The requirement of a lack of arbitrage possibilities is at the core of most theories and models in modern day finance. By precluding the possibility of arbitrage, researchers have been capable to get path breaking benefits.
No arbitrage situations can normally be derived with much less stringent specifications, than main economic models. Take for instance the case of Put-Call Parity for European alternatives on non-dividend paying stocks. It states that the distinction amongst the contact premium and the place premium, for alternatives on the very same stock and with the very same workout price tag and time till expiration, will be equal to the distinction amongst the prevailing stock price tag and the present worth of the workout price tag.
Option pricing
This is a far more standard outcome than effectively identified solution pricing models such as the Binomial Model and the Black-Scholes Model. While these models make more stringent assumptions about the evolution of the stock price tag more than time, they also rely on a no-arbitrage argument to derive the final benefits. Put-Call Parity, which needs only the absence of arbitrage, is consequently valid for all solution pricing models, irrespective of the assumptions concerning the evolution of the price tag of the underlying stock.
For instance, a stock is trading at Rs one hundred on the BSE and Rs one hundred.80 on the NSE. In principle, a trader can lift one phone and acquire a million shares on the BSE and sell an equivalent quantity right away on the NSE by yet another contact. Without factoring in transaction expenses, he stands to make a price-much less danger-much less profit of Rs 8,00,000. This is arbitrage.
Cost of transactions
In true life, traders encounter transactions expenses such as bid-ask spreads and brokerage commissions. The challenge is no matter if one can make a profit regardless of these expenses. Also, each BSE and NSE have a T+2 settlement cycle. Hence to implement such a approach, the trader will have to have prior access to sufficient money in his bank account, and sufficient shares in his Demat account.
A dealer who has sufficient sources in the kind of each securities and money, and who does not have to spend a commission to trade, may well finish up profiting from such possibilities, which usually last for fleeting moments.
Looking at an challenge from a dealer’s and an arbitrageur’s viewpoint leads to the very same conclusion. Assume a cash marketplace dealer is quoting the following prices for 3-month and six-month loans, exactly where the prices are quoted on a per annum basis.
3-M 5.22% – 5.40%
6-M 8.04% – 8.40%
The forward price for a 3-month contract should really be such that the dealer tends to make a profit no matter if he borrows for 3 months and lends for six months or borrows for six months and lends for 3 months. Thus, the forward price will have a reduce bound of 10.5377% per annum, and an upper bound of 11.4308% per annum.
The logic is based on the argument that either way the dealer ought to make a profit. Now the dealer’s borrowing price is the arbitrageur’s lending price, even though the dealer’s lending price is the arbitrageur’s borrowing price. Hence, if there’s no arbitrage profit, no matter if the arbitrageur borrows for 3 months and lends for six months, or the other way, we come to the very same conclusion.
The writer is CEO, Tarheel Consultancy Services