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Corp Finance/Derivatives > VI-Dev Pricing/Valuation-3 > Flashcards

VI-Dev Pricing/Valuation-3 Flashcards

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1
Q

investor risk type

及

要求的rate of return

附带问题：

  1. pricing asset 假设：
  2. pricing derivatives假设：
A
  1. risk aversion: 不喜欢risk，因此承担risk需要增加risk premium.

required return=rf+risk premium

  1. risk-neutral: 对risk无所谓，因此有没有risk只要求rf

required return=rf

  1. risk-seeking: 喜欢risk，为了承担risk宁可要少于rf的return。仅理论存在

required return=rf-risk premium

  1. 假设risk-aversion. 按rf+λ折现
  2. 假设risk-neutral,按rf折现
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2
Q

【Spot Price】概念

  1. discount rate折现率谁确定
  2. λ
  3. convenience yield/对forward price影响
  4. θ
  5. γ
  6. carry/ cost of carry
  7. spot price So 公式
A
  1. risk-avert investors: risk-free rate+risk premium
  2. risk premium
  3. 持有commodities无法金钱衡量的benefit，会影响spot price，对forward price: 越高使其越低。因convenience yield到底属于carrying benifit, 代入公式
  4. present value of carry cost
  5. present value of carrying benefit
  6. net of costs and benefits
  7. 见图/也可记忆为future price=
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3
Q

【So, FP, Arbitrage】

  1. FP>So(1+rf)T

怎么做？

  1. FP< So(1+rf)T

怎么做？

A
  1. 借入So资金，买入long underlying

forward short @FP

到期卖@FP，还银行So(1+rf)T

  1. 借入underlying并卖掉（short underlying）

收入So存银行

forward long @FP

到期银行取出So(1+rf)T买@FP

归还underlying

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4
Q

Arbitrage Replication

  1. 三组公式
  2. replication意义
A
  1. 见图
  2. replication is the essence of arbitrage

有时replication的transaction cost更低

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5
Q

【forward】

  1. @0, value=？
  2. @ mature, value=
  3. forward price F(0)T
  4. @t, value=
A
  1. initial value=0
  2. V(T)=S(T)-F(0)T
  3. F(0)T=S(0)T*(1+rf)T+θ(1+rf)T-γ(1+rf)T
  4. 见图
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6
Q

【FRA】

  1. FRA全称
  2. 3*9FRA @5%意思
  3. long 30d FRA underlying 90d
A
  1. forward rate agreements
  2. 3个月后以5%借入，9个月后还。实质借6个月

若3个月后的180d Libor为6%，则有gain

  1. 30天后按90-d libor借入

相当于long 120d Eurodollar deposit, short 30d Eurodollar deposit

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7
Q

【futures pricing】

  1. futures/ forward price之比较
  2. futures/ forward price与interest rate之比较
A
  1. 通常来讲price应该相同

2.

a. futures price/ r正相关，由于每日结算后的gain可以在r再投资，此时futures更受欢迎，价格更高
b. futures price/r负相关，则forward更受欢迎，价格更高

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8
Q

【swap】

  1. swap之拆解
  2. 定价的前提概念
  3. pricing思路/核心
  4. valuation思路/核心
  5. 本质：pay？receive？
A
  1. 0-t1, 0-t2, 0-t3等一系列forward,每个forward price不一定相同
  2. 上述一系列forward，按道理每个的price应该不同。实际上只要交易双方同意，可以订立一个初始value不为0的forwar contract，因此可以订立一系列forward contracts, all priced at swap price。起初的value gain/loss可以compensate at t0
  3. float rate现金流折现，再均摊至各期/replication
  4. float rate现金流折现到t，减去fixed rate现金流折现到t/replication
  5. pay variable, receive fixed
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9
Q

【Option Price】

不同因素对期权价格影响

+特别注意

A

time to expiration: 对于欧式看跌European put,

总体也应体现为时间越长，价值越高

但有时too deep in the money, higher rf,

会造成时间变长价值反而下降

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10
Q
  1. 解释time value decay
  2. 区别于time value of money
A
  1. 对于期权，距离到期时间越长，时间价值越大，靠近到期时间，时间价值逐渐下降decay
  2. time value of money相反，货币价格随时间增加而增加
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11
Q

【European Option】时间t

  1. max value call c0
  2. max value put p0
  3. min value call c0
  4. min value put p0
A
  1. St (期权价格不可能大于资产价格)
  2. X/（1+rf）T-t
  3. max (0, St - X/(1+r)T-t)
  4. max (0, X/(1+r)T-t - St)
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12
Q

【American Option】

  1. 关于early exercise问题2
  2. min value of call
  3. min value of put
  4. Ame opt与Eu opt价格比较2
A
  1. Ame call with no dividend will never early exercise

因为价格高还不如转手卖

Ame put with no div will more likely to early exercise

  1. max [0, S-X/(1+r)T]原本应该是S-X,但价格总不能比Euro call低，所以和Euro call一样
  2. max [0, X-S]
  3. Ame Opt价格总是大于等于Eur Opt

如果不存在分红，Ame call价格等于Eur Opt

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13
Q

【put-call parity】

  1. protective put
  2. fiduciary call
  3. 推导过程
  4. 公式
A
  1. 持有一个strike price=X的put, 一个股票S

初始价值p0+S0

2.持有一个strike price=X的call，一个面值X的政府债券

初始价值c0+X/(1+r)T

  1. 对于protective put，到期收到max(0, X-S),+S

即max(S,X)

对于fiduciary call，到期收到max(0, S-X)+X

即max(X,S)

两者到期收到价值相等，根据一价定律，两个资产组合现值也应相等。则有：

  1. P0+S0 = C0+X/(1+r)T
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14
Q

【put-call parity】应用

  1. 合成
  2. 套利的理解
A

套利：根据评价公式计算出c0，与市场上c价格比较，若有出入，则公式一方现价格高于另一方

买入低价一方(如long put, long bond)

卖出高价一方(如short stock, short call)

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15
Q

【put-call forward parity】

  1. 来源
  2. 公式2
A
  1. 原protective put = p+asset

将asset合成为forward price=F(0)T的远期，+面值F(0)T的纯折价债券，到期收益仍相同，因此现值仍相同

forward现值为0，则现值为

p0+F(0)T/(1+r)T

2.

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16
Q

【Binominal valuation】

  1. 原理
  2. 两个公式
  3. the volatility of the underlying is presented by
  4. 解释π
  5. d=
A
  1. 研究underlying price，价格上升时的S-X得出C1+

价格下降时C1-，以概率加权得期望值，再按risk free rate折现

  1. 见图
  2. u and d.在公式中直接体现的。标准差虽是背后的原因，但不体现在公式中
  3. π is not actual probability but risk-neutral probability
  4. d=1/u
17
Q

an arbitrage transaction

generates a net inflow of funds

A

at the start of the holding period

Corp Finance/Derivatives (6 decks)

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