reading 49. Basics of derivative pricing and valuation
49a. Explain how the concepts of arbitrage, replication and risk neutrality are used in pricing derivatives.
For most risky asset,
current value as the discounted PV of expected price of the asset at future time.
future price is subject to risk(uncertainty),the discount rate includes a risk premium with risk-free rate.
investor分为
1）risk-averse: require a positive premium (high return) on risky assets
- risk-neutral: no risk premium, discount the expected future value of an asset or future cash flows at the risk-free rate.
Value risky assets --based on no-arbitrage condition.
套利的本质就是无风险。
当投资组合的无风险回报率高于市场无风险利率，就有套利的机会。
arbitrage refers to a transaction that investor purchases one asset or portfolio of assets at one price and simultaneously sells an asset or portfolio--has the same future payoffs-regardless of future events, at a higher price
-realize a risk-free gain on the transaction
risk-neutral pricing-no-arbitrage pricing or the price under a no-arbitrage condition.
replication-the process replicate the payoffs on one asset or portfolio with those of a different asset or portfolio.
risk bond+credit protection= bond valued at the risk-free rate
风险资产+衍生品=无风险资产
Example: sell a call on the stock at 40, buy a put on the stock at 40
a. if stock price is 40 at expiration, the put and call are both worthless.
b.大于40, the call will be exercised, the stock will be delivered for 40, the put will expire worthless.
c.小于40, the put will be exercised, the stock will be delivered for 40, the call will expire worthless.
Stock+put -call=40/(1+Rf)T
put-call parity
49b. Distinguish between value and price of forward and futures contracts.
期货和远期合约在期初的价值=0
49d. Explain the value and price of forward contract are determined at expiration, during the life of the contract and at initiation.
49e. Describe monetary and non-monetary benefits and costs with holding the underlying asset and explain how they affect the value and price of a forward contract.
dividend payments on a stock or interest payments on a bond
-example of monetary benefits of holding an asset
convenience yield-nonmonetary benefits-difficult to measure--primarily commodities.
49c. calculate a forward price of an asset with 0, positive or negative net cost of carry.
net cost of carry(simply carry)=PV (benefits of holding the asset)-PV(costs of holding the asset).
net cost of carry is positive, benefits(cash flow yield and convenience yield)-costs(storage and insurance) of holding the asset
=(S0-net cost of carry)*(1+Rf)T
49f.Define a forward rate agreement and describe its uses.
FRA is a derivative contract that has a future interest rate, rather than an asset, as its underlying.
-the point of entering into an FRA-lock in a certain interest rate for borrowing or lending at some future date
一方要给另一方支付between fixed interest rate and market interest rate
LIBOR is most often used as the underlying rate.
US dollar LIBOR -rates on Eurodollar time deposits, interbank US dollar loans in london.
synthetic FRA- bank can create the same payment structure with two LIBOR loans
49g.Explain why forward and futures prices differ.
两者same function in gaining exposure to or hedging specific risks, but differ in standardization, liquidity and counterparty risk.
For pricing and valuation 方面，
futures gains and losses are settled each day,
margin balance is adjusted accordingly.
49h. Explain how swap contracts are similar to but different from a series of forward contracts.
49i. Distinguish between the value and price of swaps.
forward contract rates =swap in FRAs
based on a contract rate for the value of forward contract at initiation is 0.
off-market forward-non-zero value at initiation.
49j. Explain the exercise value, time value and moneyless of an option.
Moneyness-whether an option is in the money or out of the money.
-a.in the money: generate a postive payoff
-b.out of the money: result in a loss(negative payoff)
-c.at the money: current asset price=exercise price, generate neither a gain nor loss
intrinsic value( exercise value)of an option the maximum of 0 and the amount that the option is in the money.
time value of an option-option premium 超过intrinsic value
speculative value of option
option premium= intrinsic value +time value
49k. Identify the factors that determine the value of an option and explain how each factor affects the value of an option.
6 factors determine option prices:
1)price of the underlying asset基础资产的价值，增加而增加
in general, call option values increases when the value of the underlying asset increases.
For put options,情况相反。
2)exercise price行权价，负相关
a higher exercise price decrease the values of call options.
3）risk-free rate of interest无风险收益率 增加而增加
increase in the risk-free rate will increase call option values.正相关
。。。。。。。。。。。。。will decrease put option values.负相关
4）volatility of the underlying 基础资产的波动率
volatility makes options valuable.波动率使期权具有价值。
If no volatility in the price of the underlying asset, options=intrinsic values and time or speculative value
如果基础资产价格没有波动（价格保持不变），期权将始终=内在价值，时间价格=投机价值=0
increase in volatility of price, both put and call option 两种都上升 *有区别
5）time to expiration距离到期日时间
longer time to expiration effectively increases expected volatility and increases the value of a call option.
Less time to expiration decrease the time value of call option,所以value=intrinsic value
- costs and benefits of holding the asset持有资产的成本和好处
If there are benefits of holding the underlying asset(dividend or interest payments on securities or a convenience yield on commodities), call values 下降，put values上升
positive storage costs make it more costly to hold an asset.
-make a call option, more valuable -call holders can have long exposure to the asset without paying the costs of actually owning the asset.
puts， less valuable when storage costs are higher.
49i. Explain put-call parity for European options.欧式期权的看跌-看涨期权平价关系--基于两个组合的收益。
put-call parity for European options
-based on the payoffs of two portfolio combinations:
-fiduciary call 信托买入期权 加上protective put保护性看跌期权
fiduciary call：combination of call with exercise price and pure-discount, diskless bond that pay at maturity.X+(S-X)=S when the call is in the money.
protective put: a share of stock together with a put option on the stock
(X-S)+S=X when the put is in the money, S the put is out of money.
49n. Explain how the value of an option is determined using a one-period binomial model.
binomial model
value a one-period put option
49o.Explain under which circumstances the values of European and American options differ.