Interest rate cap = Combination of Interest rate calls : ( borrowers use when rates increase)

Interest rate Floors = Combination of Interest rate puts : ( lenders use when rates increase)

Combination of both is called a Collar

Zero cost Collar : ( Borrower go long on a cap and short on a Floor)

Option pricing principles:

S0 ,St, X, r,

Intrinsic Value prior to expiration > @ expiration

Option price – Intrinsic value = Time value or speculative value

Lower bounds: are created using Risk free bonds and underling assets for European options

European call >= max(0,So-X/(1+r)^T) = American Call ( this is because American call cannot be worth less that a European call as it can be exercised early)

European put >= max( 0,X/(1+r)^T – So)

American put >= max ( 0, X- So)

Effect of Exercise price

A call option with a higher X price cannot have a higher value than one with a lower X price

Co (X1) >= Co (X2)

A put option with lower X price cannot have higher value than put with a higher X price

Po (X2) >= Po(X2)

Increase in X price reduce value of call while its will increase the value of Put.

Effect on time to expire

American or European long term calls are worth not less than Short term ones,

Long term European put is greater or less than short term one ( due to the time value of holding the put, the put holder may not receive money till end)

Long term American put is worth not less that short term

Put Call parity

Fiduciary Call (Buy European call and Buy a bond) = Protective Put ( Buy European Put & Underlying asset)

Co + X/(1+r)^t= Po + So

Synthetic is a re allocation for above formula to get a value of Co or Po

At any time this equation does not hold there is an arbitrage opptunity,

Rule of thumb : sell over valued buy undervalued ( check on the example)

Dilemma around Early exercise of American option

Why would not it be worth?

Call

• You give away cash lose opportunity interest
• You lose the right to decide whether u need the asset at expiration

But is will be worth id the underlying pays cash flows (dividends, coupons)

Puts: it is worth exercising if the company is in bankruptcy or stock value is so low,

American put value is always greater that European normally

The value equations change with – expected cash flows for underling

Co + X/(1+r)^T = Po + ( So- Pv(CF,0,t)

The Effect of interest rate & Volatility

When the interest rates are high Value of Call will increase (better to take the option rather buying the asset) Value of Put will reduce (holder will sell and invest the cash)

But this is a minor effect,

However there is a significant effect on the volatility of the underline higher the V value of option will increase

i will post the Priciing with binomial by evenig my time 