Since the middle regime [theta] < [ECT.sub.t-k] [less than or equal to] [[theta].sub.+] can be interpreted as a no-arbitrage condition
, it allows the identification of short-term arbitrage opportunities in the lower ([ECT.sub.t-k] < [[theta].sub.-]) and in the upper ([ECT.sub.t-k] > [[theta].sub.+]) regimes, when they occur.
As noted by Blanchard and Watson (1982), when the bubble either bursts (with probability 1 - [pi]), or has a price increase with probability [pi], a non-bursting bubble has to grow at a rate 1 + r/[pi] - 1, in order to satisfy the no-arbitrage condition
and yield a net expected return r.
In fact, some have argued that because of frictions or inability to practically hedge, no-arbitrage arguments should not necessarily apply, or the no-arbitrage condition
should not be required in a fair value framework.
Under ideal conditions, the no-arbitrage condition
stipulates a relationship between short-term and long-term interest rates on securities of comparable credit quality.
First, we rewrite the no-arbitrage condition
for Northern production.
We begin with the no-arbitrage condition
. Not only does it express agents' required rates of return to both types of capital, but it also can be used to show how the accumulation of factors occurs:
We can derive the risk-neutral probabilities of the entire evolutionary process of the R&D project based on the no-arbitrage condition
. According to the estimated cash flows derived from the R&D project, its fair value can be calculated by a backward procedure with respect to the risk-neutral probabilities.
Using the expression for profits (5) in the no-arbitrage condition
(8), and rearranging terms, one can find that: (14)
In this case, the payoffs are so closely related that the price of the option is completely determined by the no-arbitrage condition
(that is, the Black-Scholes model).
To derive a closed form expression for the market value of the firm in model 1 we invoke the no-arbitrage condition
. This states that the expected returns from holding equity (the sum of dividends D and capital gains [Mathematical Expression Omitted] net of tax) must be in line with those from holding bonds (the nominal interest rate [r.sub.B] net of tax).
What is relevant is whether a no-arbitrage condition
holds which equalizes rates of return (possibly adjusted for risk) on assets in different locations.
The no-arbitrage condition
for a foreign asset with an income of X*(s) and its domestic perfect substitute yielding X*(s)e(s) is