Diluted book value per share is calculated based on total shareholders’ equity excluding the aggregate value of the liquidation preferences of our preference shares, as at December 31, 2014, 2015, 2016, 2017 and 2018, divided by the number of dilutive equivalent shares outstanding of 63,444,356, 62,240,466, 61,001,071, 60,202,409 and 60,320,879 as at December 31, 2014, 2015, 2016, 2017 and 2018, respectively. As at December 31, 2014, 2015, 2016, 2017 and 2018, there were 1,426,988, 1,322,093, 1,226,607, 728,324 and 577,723 of dilutive equivalent shares, respectively. Potentially dilutive shares outstanding are calculated using the treasury method and all relate to employee, director and investor options.
Gross written premiums. The changes in our business segments’ gross written premiums for the twelve months ended December 31, 2018, 2017 and 2016 were as follows:
Our $300 million 4.650% Senior Notes due 2023 (the “2023 Senior Notes”) and $125.0 million 6.00% Senior Notes due 2020 (the “2020 Senior Notes”) were the only material debt issued by Aspen Holdings as at December 31, 2018 and 2017 totaling $424.7 million and $549.5 million, respectively. On June 18, 2018, we elected to redeem $125.0 million in aggregate principal amount of the 2020 Senior Notes which resulted in a realized loss, or make-whole payment, of $8.6 million. In addition to the 2020 Senior Notes and 2023 Senior Notes, as at December 31, 2018 we also reported $4.6 million of debt previously issued by Silverton (2017 -$86.6 million). For further information on Silverton, refer to Note 7 of our consolidated financial statements, “Variable Interest Entities.”
Case reserves are based on a subjective judgment of facts and circumstances and are established for the purposes of internal reserving only. Accordingly, they do not represent a commitment to any course of conduct or admission of liability on our behalf in relation to any specific claim.
Exposure-based method: This method is typically used for specific large catastrophic events such as a major hurricane. All exposure is identified and we work with known market information and information from our cedants to determine a percentage of the exposure to be taken as the ultimate loss.
Overall, prior year reserve releases in 2018 increased by $5.7 million from $105.4 million in 2017 to $111.1 million. Reserve releases in the reinsurance segment in 2018 were $68.4 million compared to $81.8 million in 2017 and came from property catastrophe reinsurance, other property reinsurance and specialty reinsurance lines. Reserve releases in the insurance segment in 2018 were $42.7 million compared to $23.6 million in 2017 and came from property and casualty, and marine, aviation and energy lines.
As at December 31, 2018, we held foreign exchange contracts that were not designated as hedging under ASC 815 - “Derivatives and Hedging” with a notional amount of $1,257.3 million (2017 - $751.6 million). The foreign exchange contracts are recorded as derivatives at fair value in the balance sheet with changes recorded as a change in fair value of derivatives in the statement of operations. For the twelve months ended December 31, 2018, the impact of foreign exchange contracts on net income was a loss of $31.8 million (December 31, 2017 - gain of $27.7 million).
As at December 31, 2018, we held foreign exchange contracts that were designated as hedging under ASC 815 with a notional amount of $94.3 million (2017 - $60.6 million). The foreign exchange contracts are recorded as derivatives at fair value with the effective portion recorded in other comprehensive income and the ineffective portion recorded as a change in fair value of derivatives in the statement of operations. The contracts are considered to be effective and therefore the movement in other comprehensive income representing the effective portion was a loss of $2.1 million for the twelve months ended December 31, 2018 (December 31, 2017 - gain of $3.0 million).
The improvement in the underwriting result in 2018 compared to 2017 was due to lower catastrophe losses, a decrease in large losses and a modest increase in reserve releases. The decrease in underwriting income in 2017 compared to 2016 was due to higher catastrophe losses, lower reserve releases, an increase in large losses, an increase in attritional losses in the insurance segment and a reduction in net premiums earned partially offset by a reduction in expenses.
Ceded written premiums. Total ceded written premiums for 2018 was $1,052.1 million, an increase of $202.2 million from 2017. Ceded written premiums increased primarily due to an increase in the proportion of business ceded to our casualty, financial institutions and property quota share programs.
In 2017, the insurance segment experienced $108.7 million of catastrophe losses, consisting of $22.4 million from Hurricane Harvey, $20.6 million from Hurricane Irma, $13.2 million from Hurricane Maria, $10.2 million from wildfires in California and
Valuation of Investments, Equity Method. The value of our investments in MVI, Chaspark, Bene, Digital Re and Crop Re are based on our share of the capital position of the entities which includes income and expenses reported in quarterly management accounts. Each of MVI, Chaspark, Bene, Digital Re and Crop Re is subject to annual audit evaluating the financial statements of the entities. We periodically review the management accounts of MVI, Chaspark, Bene, Digital Re and Crop Re and evaluate the reasonableness of the valuation of our investment.
Reserves by segment. As at December 31, 2018, we had total net loss and loss adjustment expense reserves of $4,996.6 million (December 31, 2017 - $5,234.3 million). This amount represented our best estimate of the ultimate liability for payment of losses and loss adjustment expenses. Of the total gross reserves for unpaid losses of $7,074.2 million at the balance sheet date of December 31, 2018, a total of $3,969.8 million, or 56.1%, represented IBNR claims (December 31, 2017 - $3,720.8 million and 55.1%, respectively). The following tables analyze gross and net loss and loss adjustment expense reserves by business segment as at December 31, 2018 and 2017, respectively:
Operating Subsidiaries. As at December 31, 2018, the Operating Subsidiaries held $930.4 million (December 31, 2017 - $821.7 million) in cash and short-term investments that are readily realizable securities. The increase is largely due the balance held at 2017 year end being lower than in previous years due to costs associated with the increase in ceded reinsurance and the significant level of claims activity in 2017. Management monitors the value, currency and duration of cash and investments held by the Operating Subsidiaries to ensure they are able to meet their insurance and other liabilities as they become due and was satisfied that there was a comfortable margin of liquidity as at December 31, 2018 and for the foreseeable future.