Structured products gained significant popularity in the retail market since the beginning of the second decade of the 21st century, due to the steady decline in interest rates across the global economies following the GFC. This led investors to the search for yield enhancement investments. One of them is the autocallable, a type of exotic option. The autocallable has the feature to be called by the issuer if the reference asset is at or above a pre-specified level on pre-specified futures dates. The principal guarantee disappears if the underlying asset price falls below a pre-specified level. A typical autocallable option is constructed using at least two barrier options. The option with lower barrier comes in the form of an at-the-money, down-and-in put option. The option with higher barrier has a knock-out feature, meaning the product matures early if the index rises above the upper barrier, this can be represented by a long up-and-out digital/binary call. Between these two barriers, investors earn an above-market coupon during the tenor of the deal. Autocallables are quite popular in the Asian market, especially in Japan and Korea.

 

Assume the date is 25 February 2021. The Korean Composite Stock Price Index, or KOSPI, closed at 3100. The one-year risk-free rate for the Korean won is 0.8025%. KOSPI is expected to pay a dividend yield of 2% and the ex-dividend date is the 18 August 2021. The volatility of KOSPI on the same day is 27.92%. The head of structuring asks for your help with the knock-in put of the autocallable with a barrier of H. Assume a day count convention of 360 days, a cash rebate of 0 for exotics, and the expiration date for all exotics is 20 February 2022.

a. Using 10-step binomial tree and the Cox-Rubinstein-Ross parameterization, price an at-the-money (ATM) European down-and-in put with barrier (HL) set at the index level of 2900.

b. Using the Black-Scholes model, price the vanilla equivalent with the same contractual characteristics. What drives the differences between the two prices derived here and in part a? How can the two option price solutions converge?

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Balances, August 1, 2017 Issuance of common stock Net income Dividends... Balances, August 30, 2017 Cash. Accounts payable Land.. Total assets JULIE BAXTER Statement of Stockholders' Equity August 31, Year 1 Accounts receivable. Prepaid expenses Chapter 1 The Role of Accounting in Business Common Stock Common stock. Retained earnings. Total liabilities and stockholders' equity S Liabilities $100,000 Stockholders' Equity Balance Sheet For the Month Ended August 31, 20Y7 Assets Cost concept Going concern concept Matching concept 0 Statement of Cash Flows August 31, 20Y7 Cash flows from operating activities: Cash received from customers.... Cash paid for operating expenses. Net cash flows from operating activities. Cash flows from financing activities: Cash received from issuance of common stock. Dividends paid to stockholders. Net cash flows from financing activities. Net cash flow and cash balance as of August 31, 2017. Accounting Concept Accounting period concept Adequate disclosure concept Business entity concept Retained Earnings $ 7,800 134,500 12,000 $154,300 $100,000 140,300 Total $ 7,800 100,000 134,500 12,000 $254,300 $327,200 303,600 $ 51,600 17,500 60,000 $129,100 C $ 81,200 7,200 $100,000 Notation P D B G M 240,300 $328,700 E1-26 Accounting concepts Match each of the following statements with the appropriate accounting concept. Some concepts may be used more than once, while others may not be used at all. Use the nota- tions shown to indicate the appropriate accounting concept. (12,000) $ 23,600 88,000 $111,600 Balances, August 1, 2017 Issuance of common stock Net income Dividends... Balances, August 30, 2017 Cash. Accounts payable Land.. Total assets JULIE BAXTER Statement of Stockholders' Equity August 31, Year 1 Accounts receivable. Prepaid expenses Chapter 1 The Role of Accounting in Business Common Stock Common stock. Retained earnings. Total liabilities and stockholders' equity S Liabilities $100,000 Stockholders' Equity Balance Sheet For the Month Ended August 31, 20Y7 Assets Cost concept Going concern concept Matching concept 0 Statement of Cash Flows August 31, 20Y7 Cash flows from operating activities: Cash received from customers.... Cash paid for operating expenses. Net cash flows from operating activities. Cash flows from financing activities: Cash received from issuance of common stock. Dividends paid to stockholders. Net cash flows from financing activities. Net cash flow and cash balance as of August 31, 2017. Accounting Concept Accounting period concept Adequate disclosure concept Business entity concept Retained Earnings $ 7,800 134,500 12,000 $154,300 $100,000 140,300 Total $ 7,800 100,000 134,500 12,000 $254,300 $327,200 303,600 $ 51,600 17,500 60,000 $129,100 C $ 81,200 7,200 $100,000 Notation P D B G M 240,300 $328,700 E1-26 Accounting concepts Match each of the following statements with the appropriate accounting concept. Some concepts may be used more than once, while others may not be used at all. Use the nota- tions shown to indicate the appropriate accounting concept. (12,000) $ 23,600 88,000 $111,600