Forwards and Options Flashcards
Put call parity
P-C = Z*(K-F)
How cna you sue linear interpolation to find option prices
If they are European and put call parity holds then P-C for options where strikes are equally spaced will have equal step size between them
What is Z graphically
Plot P-C against strike - z is slope, should be the same if put call parity holds
What type of function are options
Convex functions of strike. Convex means. If the line segment between any two distinct points on the graph of the function lies above the graph.
Has increasing first derivative
Why doesnt Put call parity work in some cases
Arbitrage opportunity or dealing wiht american option. Put call parity only works if one exercise date
How to compute an arbitrage trade
Find forward structures C-P costs and payoffs then to get arbitrage was to hedge exposure to future share prices so you subtract forwards to get a risk free payoff
Subtracting forwards gives risk free bonds.
Arbitrage would be borrow at lower rate and invest at higher.
Other way to show : Payoff for all ranges of K an show its never negative sometimes positive.
How to show valid probability density function
Non negative, and integrates to 1
How to calculate forward value from risk neutral density
Mean of the risk neutral density
How to calculate call price from risk neutral density
Integrate 1-cdf is the undiscounted call price so we must then multiply by Z
PV get and PV pay of call otpion
ZF = PV get
ZK = PV Pay
How to find ZCB price from call option price
Differentiate and let strike go to zero then -Ce’0 = ZCB
What is risk neutral cdf in terms of call option prices
Fk=1-Ce’k/Ce’0
Relationship of cdf to pdf
Pdf = differentiated cdf
How to calculate forward value of an index from Call option price
Ce0 is an entitlement to the share at time 10. So forward value is this divided by ZCB
OR
Calculate mean of risk neutral density
Limit of BS as st dev goes to 0 or infinity
As goes to 0: max(PVget-PVPay,0)
As goes to infinity: PVGet
How to show something is strictly increasing
Show gradient in relation to variable of interest : if gradient has to be positive must be increasing formula
How to show something is concave/convex
Differentiate twice. If second derivative is positive then means convex
What does convexity mean for american call options
Call option struck at the average of two strikes is less valuable than the average of two call options one at each strike. That is the definition of convexity.
What should I check for when assessing a call option formula to be used for all strikes and extrpolated
Call options should be decreasing functions of strike. decreasing to zero - does this happen at the boundary.
How to tell without maths if Put or call option prices permit arbitrage
The call prices do not decrease for large k and the put prices are not increasing for small k
Compare put option to insurance
Buying a put option is like buying insurance against adverse effect of market falling. Insurance buyers are prepared to pay a premium, pay more than the expected claims to reduce downside risk. The same goes for options. The option buyer will pay a premium above the option payoff to reduce downside risk, espeically for extreme downside risk.
Whats the minimum and maximum value of a trade involving options
Being forced into exercise the option or if we were forced not to exercise the option so has value 0.
Max value would be options cannot be worth more than outright entitlement to the underlying
