Ibrahim Nasser Khatatbeh
Q1: Explain how the option pricing formula developed by black and scholes can be used for common stock and bond valuation. Include in your discussion the consequences of using variance applied over the option instead of actual variance.
Its generally known that Black and Scholes model became a standard in option pricing methods , with almost everything from corporate liabilities and debt instruments can be viewed as option (except some complicated instruments), we can modify the fundamental formula in order to fit the specifications of the instrument that will be valued.
An argument done by Black and Scholes which was based on the past ...view middle of the document...
With some modification of the new boundaries to the formula of Black and Scholes we can derivate a formula for valuing the bonds with specifications as mentioned above. Hence that by using the volatility assigned for the option in Black and Scholes formula , the result(values) generated by the formula will show a skewness from the actual value(mispricing problem) as in the case in which the implied volatility was bigger than actual volatility of the underlying instruments ( Equity, Bond) ,the price estimated will be discounted (decline in value referring to the negative relation between volatility and the instrument price ).
Note that some kind of bonds like (convertible, callable, ….etc) which contains more than one option can be difficult to value using Black and Scholes model without modifying the assumption of constant volatility. More research’s was done later to account for persistent stochastic volatility instead of the constant volatility which shows more accuracy of the results in predicting the actual market prices and allowing more complicated options to be valued.
Q2: Explain the discrepancies between the theoretical and empirical results for the relationship between call and put prices and how those discrepancies can be reconciled.
The theory of this relationship implies that arbitrage mechanism exists which ought to keep put and call prices in line with each other (equilibrium relationship) irrespective of the demands of buyers of options. And this relationship is based upon the argument that arbitrage opportunities would exist if there is a divergence between the value of calls and puts, if prices are out of balance (the equilibrium implied by put-call parity), traders would come to make profitable, risk-free transactions until put-call parity is restored. Hence, the theory establishes boundaries between the prices of the puts and calls that prevent arbitrage.
First, the theory assumes that trader will get a profit equal to riskless interest rate (implied by the equation (6), STOLL 1974) but in real world the market status determine the rate of interest that most paid by a borrower for the use of money that they borrow from a lender, as this will minimize or even eliminates such profit opportunities.
As the theoretical side of this relationship assumes that there are no transaction costs (the writer of an option receiving what the buyer pays) and in which the benefit to being short is equal to the cost of being long. But as the real world results observe that Transaction costs exist and are indeed high and are probably the principal reason for divergences from put-call parity. The empirical investigations assist that transaction cost doesn’t really eliminates profit opportunities, as profitable hedges still occurred, the number decreasing as the amount of transactions costs increased.
Also, other costs incurred by options traders as there looking for the options that match their specifications, which isn’t...