Pricing and Risk Analysis of Financial Derivatives

In the financial industry, derivative instruments (like options on shares, currencies or interest rates, callable bonds, caps, floors, ...) and hedging strategies have become more and more important.

Price of a European Up&Out Barrier Option as a Function of Stock Price and Time

For simple options like European vanilla options on shares paying no discrete dividends, closed pricing formulae are available. However, as the products become more complex, fast, reliable and robust numerical methods are needed. This is even more important for the valuation of larger portfolios and for short reaction times when the markets are changing.

American Option
Volatility Curve		Share Price	Calculation Results
								not-exercise
Vol Terms	Volatilities	S	Value	Delta	Gamma	Theta	Vega	probability at
								expiry
30	23.00%	60	0.03110	0.8282%	0.0019	-0.0005	0.01356	99.5106%
91	22.00%	65	0.10383	2.2799%	0.0041	-0.0013	0.03496	98.5504%
183	21.50%	70	0.28186	5.1353%	0.0074	-0.0027	0.07302	96.5131%
365	20.00%	75	0.64714	9.8367%	0.0114	-0.0048	0.12864	92.9101%
Yield Curve		80	1.29774	16.5338%	0.0153	-0.0073	0.19603	87.4285%
Terms	Yield	85	2.32857	24.9804%	0.0183	-0.0099	0.26545	80.0716%
1	5.123%	90	3.81466	34.6106%	0.0200	-0.0122	0.32426	71.1844%
30	5.126%	95	5.79625	44.6907%	0.0201	-0.0137	0.36371	61.3636%
91	5.243%	100	8.27912	54.5124%	0.0190	-0.0143	0.38011	51.3024%
182	5.255%	105	11.23498	63.5177%	0.0169	-0.0140	0.37285	41.6419%
365	5.346%	110	14.61321	71.3656%	0.0144	-0.0130	0.34700	32.8673%
730	5.391%	115	18.35192	77.9243%	0.0118	-0.0115	0.30874	25.2696%
1096	5.433%	120	22.38667	83.2264%	0.0094	-0.0098	0.26415	18.9540%
1461	5.496%	125	26.65789	87.4080%	0.0074	-0.0080	0.21854	13.8850%
1826	5.555%	130	31.11387	90.6576%	0.0057	-0.0062	0.17531	9.9325%

                             Evaluation of an American Option

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