Option Markets And Contracts Flashcards
Can use put call parity to create _________
Synthetic instruments
Put call parity
C0 + ( X ) = P0 + S0
———
(1+Rf)^T
Call+riskless bond = put + stock
Synthetic call
Put + stock - riskless discount bond
Synthetic put
= call - stock + riskless discount bond
Just rearrange put call parity
Exploit violations of put call parity by buying ____ and shorting _____
Underpriced component
Overpriced component
If fiduciary call > protective put,
Take advantage of arbitrage opp:
- sell fiduciary call
- buy protective put
Calculate option value using binomial option pricing model
- calc payoff for up and down moves
- calc exp value of option in one year as prob weighted average
- discount exp value to present at risk free rate
Given up movement, calculate down movement for stock option valuation (ie when 50% is not assumed)
D = 1/U
Calc risk neutral probability of up and down movement
Pi U = 1+Rf-D
———
U - D
Pi D = 1 - Pi U
If call option is in (out) of money, what is value?
In: tick price - t=0 price
Out: 0
Steps to evaluate option on fixed income w/ binomial tree
- Price bond at nodes w/projected int rate
- Calc intrinsic option value at each node
- Take PV of terminal option values
Assume 50% up/down
Steps to value 2 year cap or floor
Calculate expiration value of caplet/floorlet at end of y2
Bring terminal caplet/floorlets to PV
Repeat for y1
Calc value as sum of individual caplets/floorlets
Calc expiration value of caplet
1+1yr rate
Expiration value of floorlet
1+1yr rate
What are assumptions of Black-Scholes-Merton model (BSM)
- underlying asset price follows lognormal distribution
- continuous rf r constant, known
- constant known volatility of asset
- frictionless markets
- asset generates no cf
- European options
When is BSM not appropriate?
Valuing int rate options/bond prices
Underlying asset volatility not constant, known
High taxes/transaction costs
Pricing American style options
Name BSM sensitivity factors and inputs
Delta - asset price Vega - volatility Rho - risk free rate Theta - time to expiration Exercise price
Calculate delta
Delta = chg in call price
—————–
chg in stock price
For a call
For small changes in stock price, calc change in call/put price
Chg call price ~= N(d1)* chg in stock
Chg put price ~= (N(d1)-1)* chg in stock
Delta ranges from __ to __
Call is in the money at ___
Put is in the money at ___
-1 to 1
Close to 1
Close to -1
What is Delta neutral portfolio
Combo of short call options w/underlying stock
Value of portfolio doesn’t change when value of stock changes
Requires readjusting to maintain hedge
Calc num call options needed to delta hedge
Delta of call option
What does gamma measure
Rate of change in delta as underlying stock price changes
Largest w/option at the money
Put call parity for options on forwards and futures
C0 + X - Ft = P0
——-
(1+Rf)^T
