Gold mining company DigBig is issuing a gold-linked note with a maturity of 2 years. The current gold price is $1300/oz. The payout of the note is displayed in the figure below. The continuously compounded risk free rate equals 4% annualized. The note is constructed from a zero-coupon bond with a par value equal to the current gold price, and some plain vanilla European put and call options with strikes of 1000, 1300 and 1500. The note will be priced at par (= $1300) initially. 1500 1480 1460 1440 1420 Note Payout($) 1400 1380 1360 1340 1320 1000 1500 1600 1300 900 1100 1200 1300 1400 Gold Price at Maturity ($ioz) a) What are the securities needed to replicate the payout of the note? b) What is the current price of the bond position? c) If the Black-Scholes assumptions are true and the volatility of gold is 25% annualized, what is the price of the lowest strike option? d) Suppose the prices of the options are given by the table below. Does DigBig offer the note at a fair price? Strike Call Price ($) Put Price ($) 900 501.7462 32.5509 1000 431.3411 54.4574 1100 368.1737 83.6017 1200 312.3475 120.0871 1300 263.6380 163.6892 1400 221.5925 213.9554 1500 185.6215 270.2960 1600 155.0718 332.0580