OPTION PRICING USING SPOT TREE

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OPTION PRICING USING SPOT TREE

• Professor Dr. Sankaran
• Group members Xian Pang
• Yihong Chavez
• Hien Nguyen

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Local Expectations Hypothesis (LEH)

• Local Expectations Hypothesis (LEH) all bonds
  provide the same expected rate of return over
  very small holding periods.
• Pure Expectations Hypothesis the holding period
  return is the same regardless of the maturities
  of the securities. This is true for all holding
  periods.
• The theory of Pure Expectation Hypothesis is true
  only for very short, immediate holding periods.

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Local Expectations Hypothesis (cont.)

• Where rt is the return on a bond maturing at t1.
  
• This holds regardless of T.
• The expected one-period return during t, t1
  maturing at date T is equal to the one-period
  return rt at date t maturing at date t1.
• No-arbitrage
• Ex If one-period return on a 1-year bond is 6,
  according to the LEH, the one-period return on a
  10-year bond must be 6 to avoid arbitrage.

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Spot Tree Computation

• For t1
• Using Solver tool on the excel, we could solve
  this equations

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Spot Tree Computation (cont.)

• For t2
• Assumption Volatility is the same at each node
• Using solver tool in excel to solve for r at each
  node

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Spot Tree Computation (cont.)

• For t3
• Assumption Volatility is the same at each node
• Using solver tool in excel to solve for r at each
  node

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Spot Tree Computation (cont.)

• For t3 (cont.)

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Spot Tree Computation (cont.)

• For t4
• Similar method is used to compute the spot rate
  at each node
• The complete Spot Rate Tree is presented in the
  next slide

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Spot Rate Tree
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Price for Zero Coupon Matured at Time 2
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Price for Zero Coupon Matured at Time 3
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Price for Zero Coupon Matured at Time 4
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Price for Zero Coupon Matured at Time 5
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Price of Option

• 4-year European Call Option
• Option mature in 4 years
• Option written on 5-year zero coupon bond
• Bond price is 88.688
• Strike Price is 88.688

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Price of Option
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• Questions?
• Comments?

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• Thank you very much!!!
• ?