##### StickyKurtosis

##### Risk-Neutrality in Derivative Pricing

Remember that the value of an option is not affected by the real-world probabilities of the underlying price increments or decrements but rather by the expected volatilities (\(R^u\) and \(R^d\) ), which are required to price an option. We can…

##### One-Period Binomial Model

The law of arbitrage dictates that the value of any two assets (or portfolio of assets) whose payoffs are identical in all possible future scenarios at a given time must also be identical today. Unlike forward commitments that offer symmetric…

##### Put-Call Forward Parity

The put-call forward parity extends the put-call parity to include the forward contracts. To get the put-call forward parity, we substitute the present value of the forward price, \(F_0(T)\), for the underlying price:$$F_0(T)\left(1+r\right)^{-T}+p_0=c_0+X\left(1+r\right)^{-T}$$ Deriving Put-Call Forward Parity Consider an investor…

##### Put-Call Parity

Put-call parity is a no-arbitrage concept. It involves a combination of cash and derivative instruments in a portfolio. Put-call parity allows pricing and valuation of these positions without directly modeling them using non-arbitrage conditions. Deriving Put-Call Parity Consider an investor…

##### Factors that Determine the Value of an Option

The factors that affect the value of an option include the value of the underlying, exercise price, time to maturity, risk-free rate, volatility, and income or cost associated with the underlying. Value of the Underlying The value of the underlying…

##### Arbitrage in Contingent Claims

Recall that arbitrage opportunities occur if the law of one price does not hold. The no-arbitrage conditions in options are based on the payoff at maturity. Unlike forward commitments with symmetric profiles (as presented earlier), contingent claims have asymmetric payoff…

##### Exercise Value, Moneyness, and Time Value of an Option

Options are derivative instruments that give the option buyer the right, but not the obligation, to buy (call option) or sell (put option) an asset from (or to) the option seller at a fixed price on or before expiration. In…

##### Price and Value of Swaps

Remember that a swap contract involves a series of periodic settlements with a final settlement at maturity. Swap price (or par swap rate) is a periodic fixed rate that equates the present value (PV) of all future expected floating cash…

##### Comparison of Swaps and Forward Contracts

Recall that a swap is a derivative contract between two counterparties to exchange a series of future cash flows. In comparison, a forward contract is also an agreement between two counterparties to exchange a single cash flow at a later…

##### Value and Price of Futures Contracts

Recall that during the initiation of a forward commitment, no cash changes hands. Further, the forward commitment is neither a liability nor an asset to a buyer or the seller. As such, the value of both the forward contract and…