BASFIN 2 Finals reviewer [Computations]
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BASFIN 2 FINALS REVIEWER
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BASFIN 2 Finals reviewer [Computations]
- 1. 𝐶𝑎𝑠ℎ 𝐶𝑦𝑐𝑙𝑒 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 + 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 − 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑎𝑦𝑠 𝑖𝑛 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 = 𝑆𝑡𝑎𝑟𝑡 𝑜𝑓 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝐶𝑂𝐺𝑆 365 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝑅𝑒𝑐𝑖𝑒𝑣𝑎𝑏𝑙𝑒 𝑎𝑡 𝑆𝑡𝑎𝑟𝑡 𝐴𝑛𝑛𝑢𝑎𝑙 𝑆𝑎𝑙𝑒𝑠 365 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝑃𝑎𝑦𝑎𝑏𝑙𝑒𝑠 𝑎𝑡 𝑆𝑡𝑎𝑟𝑡 𝐶𝑂𝐺𝑆 365 𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑟𝑒𝑡𝑎𝑖𝑛𝑒𝑑 𝑒𝑎𝑟𝑛𝑖𝑛𝑔 𝑛𝑒𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 𝑆𝑢𝑏𝑠𝑡𝑎𝑛𝑡𝑖𝑎𝑙 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑝𝑙𝑜𝑤𝑏𝑎𝑐𝑘 𝑟𝑎𝑡𝑜 × 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 𝑆𝑢𝑏𝑠𝑡𝑎𝑛𝑡𝑖𝑎𝑙 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑅𝑒𝑡𝑎𝑖𝑛𝑒𝑑 𝐸𝑎𝑟𝑖𝑛𝑔𝑠 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 × 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑆ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟! 𝑠 𝐸𝑞𝑢𝑖𝑡𝑦 𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑂𝑟𝑑𝑒𝑟 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑄 = 2 × 𝑆𝑎𝑙𝑒𝑠 × 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟 𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑂𝑟𝑑𝑒𝑟 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 (𝑁) = 𝑠𝑎𝑙𝑒𝑠 𝑄 𝐴𝑛𝑛𝑢𝑎𝑙 𝑂𝑟𝑑𝑒𝑟 𝐶𝑜𝑠𝑡 = 𝑁 × 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑑𝑒𝑟 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝐴𝑛𝑛𝑢𝑎𝑙 𝑅𝑎𝑡𝑒 = 1 + 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 !"# !"#$% !"#$ !"#$%& − 1 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑝 × 𝑃𝑉 𝑅𝑒𝑣 − 𝐶𝑜𝑠𝑡 − 1 − 𝑝 × 𝑃𝑉 𝐶𝑜𝑠𝑡 𝐵𝑟𝑒𝑎𝑘 𝐸𝑣𝑒𝑛 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 (𝑝) = 𝑃𝑉 𝐶𝑜𝑠𝑡 𝑃𝑉 𝑅𝑒𝑣 Call Option Buyer Seller Expectation MP↑ MP↓ Loss Limited to OP Unlimited Profit Unlimited Limited to OP Put Option Buyer Seller Expectation MP↓ MP↑ Loss Limited to OP Limited to Stock Price Profit Limited to Stock Price Limited to OP At the money In the Money Out the Money (breakeven) (to exercise) (not to exercise) EP = MP EP < MP: call option EP > MP: put option EP < MP: put option EP > MP: call option 1) Underlying Price 2) Strike Price More in the money Higher OP More out the money Lower OP 3) Volatility More Volatile Higher OP Less Volatile Lower OP 4) Expiration Time Longer Expiration Time Higher OP Shorter Expiration Time Lower OP 5) Interest Rate 6) Dividends
- 2. 𝐵𝑟𝑒𝑎𝑘 𝐸𝑣𝑒𝑛 = 𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝐿𝑒𝑎𝑠𝑒 𝑎𝑓𝑡𝑒𝑟 𝑇𝑎𝑥 (𝐶) (1 + 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒) 𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝑅𝑒𝑛𝑡 𝐴𝑓𝑡𝑒𝑟 𝑇𝑎𝑥 = 𝐶 1 𝑟 − 1 𝑟 1 + 𝑟 1 + 𝑟 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 = 𝐶! + 𝐶! 1 + 𝑟 ! + 𝐶! 1 + 𝑟 ! + ⋯ + 𝐶! 1 + 𝑟 ! 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑅𝑎𝑡𝑒 = 𝑇!"#$%&'( 1 − 𝑇!"#$"#%&'"( 𝐷𝑒𝑝𝑟𝑖𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑 = 𝐷𝑒𝑝𝑟𝑖𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝐴𝑚𝑜𝑢𝑛𝑡 × 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝐷𝑒𝑝𝑟𝑖𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝐴𝑚𝑜𝑢𝑛𝑡 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡 × 𝑑𝑒𝑝𝑟𝑖𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐴𝑓𝑡𝑒𝑟 𝑇𝑎𝑥 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 = 𝑃𝑟𝑒 𝑇𝑎𝑥 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 1 − 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝐵𝑒𝑓𝑜𝑟𝑒 𝑇𝑎𝑥 𝑃𝑎𝑦𝑒𝑚𝑒𝑛𝑡 = 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 1 − 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡 + 𝑑𝑒𝑝𝑟𝑖𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑓 + 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑎𝑑𝑚𝑖𝑛 𝑐𝑜𝑠𝑡 BINOMIAL TREE REPLICATING PORTFOLIO CALL OPTION PUT OPTION ∆!"## = 𝑉! − 0 𝑈 − 𝐷 ∆!"# = 0 − 𝑉! 𝑈 − 𝐷 𝐵!"## = ∆ 𝑈 − 𝑉! 𝑅 𝐵!"# = −∆ 𝐷 − 𝑉! 𝑅 𝐶 = ∆𝑆 − 𝐵 𝑃 = ∆𝑆 + 𝐵 RISK NEUTRAL CALL OPTION PUT OPTION 𝑝 = 𝑅 − 𝑆! 𝑆! − 𝑆! 𝑝 = 𝑅 − 𝑆! 𝑆! − 𝑆! 𝐵!"## = 𝑝 𝑉! + (1 − 𝑝)(0) 𝐵!"# = 𝑝 0 + (1 − 𝑝)(𝑉!) 𝐶 = 𝐵 𝑅 𝑃 = 𝐵 𝑅 Stock Price MP Rise (U) EP – MP Fall = Vd MP Rise – EP = Vu MP Fall (D) Stock Price MP Rise (U) Stock Price = Sd = Su MP Fall (D) Stock Price
- 3. PUT CALL PARTY 𝑃 = 𝐶 + 𝑃𝑉 𝑥 − 𝑆 𝑃𝑉 𝑥 = 𝑋 𝑅 P = put value C = call value PV(x) = present value of exercise price S = stock price X = exercise price BLACK SCHOLE • Only for European option 𝐵𝑙𝑎𝑐𝑘 𝑆𝑐ℎ𝑜𝑙𝑒𝑠 = 𝑆𝑁 𝑑! − 𝐾𝑒!!" 𝑁 𝑑! N(d1) = probability of what you get S = stock price K = exercise price / strike price e-‐rt = discount factor N(d2) = probability of what you give To get the two probabilities (d1 and d2) 𝑑! = 𝑙𝑛 𝑆 𝐾 + 𝑟 + 𝜎! 2 𝑡 𝜎 𝑡 𝑑! = 𝑙𝑛 𝑆 𝐾 + 𝑟 − 𝜎! 2 𝑡 𝜎 𝑡 OR 𝑑! = 𝑑! − 𝜎 𝑡