under these assumption The Black-Scholes assumptions below are made in this problem: (1) calls and puts are European style; (2) both the call and the put share the same underlying, which is none-dividend paying; (3) expiry ܶstrike ܭ ,and interest rate ݎ are the same for both the call and the put.
show that the call and the put share the same vega, i.e., please prove the following equality.
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= ܥ ߪ݀
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ܲ ߪ݀